Let's dive right in:

JLPT N3: ことは～が (it's true that... but...; I did do... but...)

We can also rewrite that as:

X ことは X が

With this construction, the speaker inserts the same phrase before and after ことは in order to (1) acknowledge a fact and (2) indicate that this fact is not very important. Typically a phrase will come after が explaining why the fact before and after ことは is not all that important.

...and if you can understand grammar points just by reading explanations like that, I think you might be a genius. Personally, I've always learned better from examples...

説明書を読んだことは読んだが、まったく意味が分からなかった。
せつめいしょ　を　よんだ　ことは　よんだ　が、　まったく　いみ　が　わからなかった。
Although I did read the instructions, I didn’t understand them at all.
Literally: “instructions + を + read + こと + は + read + が, + not at all + meaning + が + didn’t understand.”

In this sentence, the acknowledged fact that is not all that important is（説明書を）読んだ, "(I) read (the instructions)." It looks very strange if we insert some English words:

Read the instructions ことは read が, I didn't understand them at all.

A quasi-literal translation of that might be:

As for reading the instructions, I read them, but I didn't understand them at all.

In more natural English, that becomes something like:

I read the instructions, but I didn't understand them at all.
I did read the instructions, but I didn't understand them at all.
While I did read the instructions, I didn't understand them at all.
Although I did read the instructions, I didn’t understand them at all.

It is often quite difficult to include the nuance of ことは～が in an English translation.

Sometimes, though, we can express the nuance of this Japanese by using verbs like "do" and "is." Take a look at "do cook" in the following English translation:

料理はすることはするんですが、レシピを見ないと何も作れないんです。
りょうり　は　する　ことは　する　んです　が、　レシピ　を　みないと　なにも　つくれない　んです。
I do cook, but I can’t make anything without a recipe.
Literally: “cooking + は + do + こと + は + do + んです + が, + recipe + を + don’t look at + と + nothing + cannot cook + んです.”

When I first came across this grammar point, I had a very hard time wrapping my head around it. Now I'm trying to explain it, and it seems simple and straightforward to me. I suppose advancing to fluency is a bit like that--I don't know what happened, but I understand things now. ^^

But it still seems a bit strange to me that we can say something like, "As for cooking, I cook, but I can't make anything without a recipe."

To be fair, explaining how a verb like "do" in the above translation adds emphasis can be difficult, too. I had to teach a lesson on that once when I was an English teacher in Japan, and students had a very hard time with it.

While we're on the topic of things that are hard for me to explain, let's talk about the んです that we saw in the previous sentence:

料理はすることはするんですが、レシピを見ないと何も作れないんです。
りょうり　は　する　ことは　する　んです　が、　レシピ　を　みないと　なにも　つくれない　んです。
I do cook, but I can’t make anything without a recipe.
Literally: “cooking + は + do + こと + は + do + んです + が, + recipe + を + don’t look at + と + nothing + cannot cook + んです.”

I hate trying to explain んです、んだ、のです、and so on because it is very hard to put this ん／の into English.

In this specific type of sentence, んです is just adding emphasis to the phrase coming before it.

However, don't go thinking that んです is only used to add emphasis to things! Mastering all of its uses and nuances is enough to make my head spin. These other lessons might help:

[NDL #426] - Basics: Feminine の
[NDL #433] - Basics: Intro to んだ
How to Say “So I was thinking…” in Japanese

👷 Construction 👷

The only thing you really need to worry about when making ことは～が sentences is that the word before ことは must be in the plain form. So far, we've seen plain form verbs 読んだ (read) and する (do), but we can also have words that are not verbs.

For example, here we have an i-adjective (in plain form) before ことは：

わたしの犬は可愛いことは可愛いんですが、散歩が嫌いで困っているんです。
わたし　の　いぬ　は　かわいい　ことは　かわいい　んです　が、　さんぽ　が　きらい　で　こまっている　んです。
My dog is cute, but he doesn’t like walking, and I’m not sure what to do about it.
Literally: “I + の + dog + は + cute + こと + は + cute + んです + が, + walk + が + disliked + で + am troubled by / am worried about + んです.”
Note: For the English to have the same nuance as the ことは～が formation, the word "is" would have to be stressed.

Also, you may have noticed that the verbs in our sentences have all been the same tense. For example, we had 読んだ...読んだ and する...する.

When talking about things that happened in the past, though, sometimes the first verb will be in the present plain tense while the second verb is in the past tense:

新年会に参加することはしたのですが、１杯だけ飲んで帰りました。
しんねんかい　に　さんか　する　ことは　した　のです　が、　いっぱい　だけ　のんで　かえりました。
While I did go to the beginning-of-the-year party, I only had one drink and then went home.
Literally: “New Year party / beginning-of-the-year party + に + participation + do + こと + は + did + のです + が, + one drink + only + drink (and) + went home.”
Note: I also mentioned this in a recent lesson, but a 新年会 is not a New Year's Eve party. It is a party that takes place in the New Year.

That's all for this one!

If you're thinking...

As for reading this lesson, I read it, but it still doesn't make sense to me.

...then maybe try rereading it. Or just wait until you have a better sense of Japanese... and hope that once you do, this stuff will start making a lot more sense... like it did for me. ^^