Translation:I like cabbage, especially red cabbage.
There's no such word as "espécialement". The word is "spécialement" meaning "specially"/"especially".
"surtout" can mean either "above all" or "especially". "above all" indicates a favourite, "especially" a preference.
"I like cabbage, especially red cabbage but above all pickled cabbage". "surtout" seems to have the milder meaning here.
This is correct that "aimer" covers like and love. In the case of cabbage, I think that "like" is the best choice unless there is a king of passion for it. As a side note, if you want to tell to someone that you like him or her very much but without loving him, you can say : "je t'aime bien".
Well I do not totally agree. "aimer" means love only when it is matter of people. When it is object, then love -> "adorer". If you say "J'aime le chou" everybody will understand that you "somehow" like it. If you want to say that you do love cabbage you need to be more specific, either with "adorer" or with an adverb ("j'aime beaucoup le chou" "j'aime énormément le chou" ...)
By the way, that's funny that an adverb can turn "like" into "love" with things, because it can do the opposite with people. In "L'amour en fuite" (the last in Truffaut's Antoine Doinel series that began with Les 400 coups), Colette says to Antoine "Je vous aimais bien Antoine, je ne vous aimais pas" ("I liked you Antoine; I didn't love you.")