My favourite dish is hot dogs. Or My favourite dish are hot dogs.?

You ask a good question because the verb "to be" should match number between subject and object. A=B is a mathematical way of explaining. the child is a student. The student is a child. NOT The student is children-children ARE students/students are children.

The way we explain this away in grammar is that "hot dogs" is a dish, a meal, rather than separate hot dogs. that is one of the problems with grammar, we do things that do not fit the rules, so we pretend that there is a hidden (unstated) meaning that allows the sentence to fit the rules.

"My favorite dish is hot dogs" is acceptable. It is the same as "my favorite dish is chicken and rice". chicken and rice is a dish, not chicken AND rice, each/separate, which would be plural. it would then have to be my favorite dishes are...

My favourite dish is hot dogs. You are talking about one dish, so you use "is".

My favorite dish is hot dog.


(example)

1. My favorite fruit is apple.
2. My favorite sweet is chocolate.
3. My favorite sport is swimming.

The verbs always becomes singular or plural based on the subject, since "dish" is the subject and its singular it would be "my favorite dish is hot dogs"

buster wrote:
"...because the verb "to be" should match number between subject and object"

This is not true. The verb 'to be' takes the nominative case in the subject and object BUT NOT number (that is singular/plural). e.g.
A teacher is many things to his students: knowledge-giver, mentor, parent, and counsellor.

According to buster, this would have to read:
Teachers are many things...
OR
A teacher is a/one thing.....!!!!!!!!!!!!