What's the deal with "icing" vs. "frosting"? Amirite? Ha ha ha! The zings just don't stop! No one says "frosting", I guess that's the deal.
Even by its creators, Zelda II is typically thought of as a mostly frosting-free game (hey it's worth using the less common word for alliteration's sake... though sometimes I feel like I alliterate way too much. I'm not Señor Seuss here), or, that is to say, largely a tangent. With only one example to build from, it wasn't yet clear which were the definitive elements of The Legend of Zelda (game) and which would be desirably repeatable elements of The Legend of Zelda (series). Zelda was just a... thing, a flavor, and it was up to the sequels to turn that flavor into a permutable recipe. In just about every sense, Zelda II is a far better game than its predecessor (not only does it not blow, it's outright awesome), but as a Zelda game it goes down decidedly funny. It's kinda like those bullshit foods out there these days like chocolate-covered bacon or cheese sandwiches with strawberry sauce. Sure it tastes awesome, but what the fuck, man?
So what Zelda II does is give a little nod to the adventure elements of its mom while constructing a layered experience built upon hardcore platforming, risk/reward role-playing, and action combat featuring an expanding array of combat techniques, ammo/health management, and learning the nuances of individual mini-boss enemies and rooms. It treats the puzzle-item collection, dungeon discovery, and hint-decryption as the formative elements of the Zelda icing - these are elements that are recycled (or even simplified) from the first game, not particularly expanded or rebuilt from scratch, not expected to form a core gameplay experience. They're just a bit of color, the little touches that make the game Zelda. That is the recipe of Zelda II: action-combat role-playing as the core cake layers and a bit of adventuring and maze-solution spread on top. Not too crazy when you think about it like that.