I can't say I have a great handle on the particulars of particle use either! For me, learning Japanese words is not a problem, nor Kanji (as I know some Chinese already)-- it's the grammar that I find especially challenging, it being so different from English. I've two books on my shelf that are entirely devoted to just explaining particles!
I'm no authority (self-studying Japanese from books mostly-- no official classes as I've no time), but my understanding is thus: では is a double particle composed of で and は, the latter being the usual topic particle. で in this case functions as a particle indicating range of topic under discussion (Japanese foods in this case). が indicates the subject of the verb (the cupola だ, or です in polite speech or 丁寧語
teineigo), which isn't always the same as the topic marked by は.
While the individual characters 好and 物 do not refer specifically to food at all, the Japanese combination word 好物 koubutsu refers specifically to a favorite FOOD or dish in particular.