Xjyuk

I'm sure there are plenty of resources on this topic, but I don't know what keywords to use to find them.

I want to know how you might create a noun by saying that the noun does something.

For example,

I saw the cow that ate vegetables at the shop

Would be something like

店で[牛は野菜を食べた]を見た。

The bracketed part of the above sentence is the clause that I don't know how to turn into a noun.

Note that I'm not looking for a sentence like

店で牛は野菜を食べていることを見た。

That would mean

I saw the cow eating vegetables at the shop

Because the cow did not eat the vegetables while I saw it, that's just how I'm identifying the cow.

Hopefully, the question is clear. Thanks in advance.

Edit
Even a name for what this is called so that I can do further reading would be invaluable.

The grammatical term you're looking for is relative clause (関係代名詞 or 連体修飾節 in Japanese).

With this keyword, you should be able to find enough articles, but this answer is a good starter: https://japanese.stackexchange.com/a/14550/5010

Thanks to @ZLK 's comment @naruto 's answer:

These are called relative clauses. They're constructed by simply writing the clause without the subject and then placing the subject afterwards.

Thus,

At the shop I saw the cow that ate vegetables

becomes

店で野菜を食べた牛を見ました。

In addition to naruto's answer, I'd like to point out that the relative clause "that" that's used in English (even in this very sentence) doesn't exist in Japanese, simply because the structure of the language is different.

It might be easier to explain using examples.

Let's look at your sample sentence in English.

I saw the cow that ate vegetables at the shop.

(I assume here that you mean you saw the cow ... at the shop, and not that the cow ... ate vegetables at the shop.)

Here, the phrase that ate the vegetables describes something about the cow. If we rephrase this as an independent statement, the cow ate vegetables. Translated to Japanese, 牛【うし】は野菜【やさい】を食【た】べた.

If we want to say something else about the cow, and use the vegetable eating as a description of the cow, in English we turn it into a relative clause, and use that "that" to connect the clause to the noun.

In Japanese, however, we don't need the "that". Verbs and verb phrases can directly modify nouns, so we just stick the whole verb phrase in front of the noun.

So if we want to turn the independent statement,

牛【うし】は野菜【やさい】を食【た】べた

... into a relative clause in Japanese, we get:

野菜【やさい】を食【た】べた牛【うし】

Literally, the vegetables-ate cow.

For your simpler sentence, you're just saying:

I saw the cow ... at the store.

店【みせ】で...牛【うし】を見【み】た。

To add our clause to describe more about the cow, we just add that in at the ... Again, English requires the "that", but Japanese doesn't:

I saw the cow that ate vegetables at the store.

店【みせ】で野菜【やさい】を食【た】べた牛【うし】を見【み】た。