Noodle: a narrow strip of unleavened egg dough that has been rolled thin and dried, boiled, and served alone or in soups, casseroles, etc.; a ribbon-shaped pasta.
Seeing as 'noodle' is only one strip, the whole dish consists of many strips and should be referred to as 'noodles'
HOWEVER, because you're only referring to ONE favourite food, the 'dish' as a whole is still singular. This is why you use 'is' instead of 'are'. If you have more than one favourite food, then you would use 'are':
My favourite foods ARE noodles and boiled eggs.
Referring to apples, 'your favourite fruit is apples' would be the correct way of saying it.