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It's impossible to declare one apple to be the best for apple cake (or pie) as there are 7500 known cultivars of apple and no one can test all of them.
See Kenji's analysis on ten apples for apple pie:
Some cultivars are highly regional and many do not keep well, so they are relatively unknown outside of their normal area of cultivation. The Gravenstein apple is one such cultivar that is largely a West Coast favorite (its season is rather short).
Moreover, for some recipes, you may want an mushier/mealier apple, for others, you might prefer something that holds its shape and texture.
CV is of course correct but I will throw in a vote for Cortland, my favorite all around apple. Great for baking( they do not deteriorate into mush) or out of hand. A NY state variety, probably available at least through out the northeast. This is an older variety, developed and first marketed in the early 1900's.
BerryBaby is trusted source on General Cooking
Depends on what texture and taste you want. I like Granny Smith, tart, firm texture. For eating I like Sweet Tangos, Honey Crisp and Fuji....sweet, crisp. A great site for Apple information dish.allrecipes.com
AntoniaJames is a trusted source on Bread/Baking.
I prefer Braeburns and Jonagolds for apple cake; when they are not available at my farmers' market, I use Honeycrisps or Fujis. ;o)
I'd suggest Golden Delicious. Not a favorite for eating in general, but great for a quick Apple Galette (see Jacques Pepin's recipe in Heart and Soul in the Kitchen) or a Philadelphia Jewish Apple Cake.
Let's keep this simple. If I had only one to pick, Honey Crisp would win .
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