Preheat the oven to 350°F. Lightly grease the bottom of an 8" or 9" springform pan or round cake pan (this will help the parchment adhere), then line the bottom with a parchment round. Generously butter the parchment and sides of the pan with the softened butter. Sprinkle with the sliced almonds, a bit at a time, pressing gently to adhere them to the pan. Your coating won’t be perfectly even, and that’s OK.

Weigh your flours; or measure them by gently spooning into a cup, then sweeping off any excess. In a medium bowl, whisk together the flours, baking powder, and salt.

In a large bowl, whisk together the melted butter, eggs, sugar, and extract until creamy, lighter in color, and slightly foamy, about 30 seconds to 1 minute. Whisk in the dry ingredients until just combined.

Use a rubber spatula to fold the apples into the batter until evenly coated. (It will look like there isn’t much batter, but don’t panic.)

Scrape the batter into the prepared pan and use your spatula to nudge the apples into a mostly-even layer.

Bake until golden-brown on top and a toothpick or paring knife inserted into the center comes out clean, about 50 to 55 minutes.

Remove the cake from the oven and let cool for 15 minutes on a wire rack. Run a paring knife or offset spatula around the edges of pan, then, if using a springform, release sides of pan; or, if using a cake pan, invert it onto a rack or plate, remove the parchment, and turn it back over, top-side up, onto a wire rack. Let cool for at least 15 minutes more. For the neatest pieces, slice with a sharp serrated knife, which will help you saw through the apple pieces rather than crushing them.