What is the difference if we say: 这是我妈妈做的菜 and 这是我妈妈的菜? With\without (做)
This is my mom's cooking
This is my mom's (cooked) dishes
This is my mom's vegetable
This is my mom's dishes
so the second version only indicates "possession". The first one indicates the "cooking" action.
The phrase can be a slang:
It is my mom's favorite
It is 小明's favorite
or depending on the context, it can commonly mean
It is my mom's favorite guy
It is 小明's favorite (type of) girl
In this case, it is similar to "my cup of tea" in English. But since it is a slang, you may need to use it carefully, such as, if you say that in front of somebody's mom, there is a chance that she may view you as impolite.
Grammatically, 我妈妈做的菜 is a defining relative clause, whereas 我妈妈的菜 is a noun phrase (possessive).
In English, a relative clause is introduced by a relative pronoun, which/ that, and it comes after the noun it describes
the dish that my mother made
the picture that my child painted
In Chinese grammar, a defining relative clause looks like an adjective, and it comes before the noun it describes.
我妈妈做的菜 My-mother-made 的 dish
我孩子畫的畫 My-child-painted 的 picture
Without the verb, it is a simple possessive xx 的 yy, where yy belongs to xx.
我妈妈的菜 my mother's dish
我孩子的畫 my child's picture
做 is a verb for 'make'
我妈妈做 = My mother makes
的 in "我妈妈做的" is an 'adjective marker' that marks [我妈妈做] as an [adjectival phrase] that modifies the noun [菜]
[我妈妈做的][菜] = [dish] [that my mother made]
的 in 我妈妈的菜 is a 'possessive marker' that marks the object 菜 belongs to the subject 我妈妈
我妈妈的菜 = 'my mother's dish' (she owns it by ordering it, made it or any other method)
It can also mean 'my mother preferred dish' (dish can be a metaphor for love-interest)
[我的][槍] = [my] [gun]
[我買的][槍] = [gun] [that I bought]
It's essentially what dROOOze mentioned in the comments:
This is the dish my mother cooked.
This implies that 我妈妈 cooked [做] the dish, and can be contrasted with dishes 我妈妈 didn't cook. Perhaps they're at a family dinner where many people bring dishes, and the child is pointing out which dish 我妈妈 cooked.
This is my mother's dish.
The emphasis here is ownership: this dish belongs to 我妈妈 in some (unspecified) way. Perhaps she purchased this dish, perhaps she cooked this dish, perhaps she invented this dish, perhaps this dish is adjusted to 我妈妈's taste (e.g. extra spicy). I feel the context is most likely a waiter at a restaurant coming out with the dish, and the child is saying 我妈妈 ordered it.
(Note: we can't tell how many dishes there are; maybe one dish, maybe more than one dish. For simplicity, I assume there's one dish.)
Though sounds similar, the latter sentence can lead to confusion - this is my mother's dish, does it mean her (favorite) dish or a dish (prepared) for her only? So I won't omit the word "做", which clearly indicates the dish was made by your mother.
A side note, in these days, you shall avoid saying "那"是我妈妈的菜 unless your finger is pointing to that dish as well. As people might take the wrong way - "that is my mother's (favorite) dish" or worse "that is my mother's love(er)" :)
Joking indeed! :)