It's fine. For many years, the American Dairy Association used the slogan "Nature's most nearly perfect food is milk." As Phil notes, "Eggs are my favorite food" is also correct. I don't happen to think that either way is better. "My favorite food is eggs" puts the emphasis on "my favorite food." "Eggs are my favorite food" puts the emphasis on "eggs." If someone asked me "What is your favorite food?" I would probably say "My favorite food is eggs." But if someone asked me "Do you like eggs?" I would probably answer "Yes, I do. In fact, eggs are my favorite food." (Actually I like eggs a lot, but eggs are not my favorite food. My favorite food is ice cream).

Hmmm... now that I think about it, although your sentence is perfectly natural and "native sounding," it might be better stylistically to say "Eggs are my favorite food."

Perfectly natural English -- the verb agrees with "food," the formal subject. Now, if you were learning Spanish, the verb would agree with "eggs," the conceptual subject.

The only thing strange about this sentence to an American is the British spelling of "favorite". Otherwise the sentence is perfectly natural.

No, it's not strange at all. The subject (food) matches the verb (is). The plural form "eggs" doesn't affect this.