Step 1In a large saute pan, melt the butter over medium heat. Stir in the apples, then the sugar and salt, tossing to coat. Cook, stirring often, until the apples are just softened, about 6 minutes. Remove from heat and spread out the apples on a rimmed baking sheet to stop the cooking process. Set aside to cool.
Step 1Heat the oven to 350 degrees. Grease a 10-by-3-inch round cake pan and line bottom with parchment paper.
Step 2In a large bowl, sift together the almond meal, whole-wheat flour, all-purpose flour, cornmeal, baking powder and salt. Set aside.
Step 3In the bowl of a stand mixer using the paddle attachment, or in a large bowl using an electric mixer, beat the butter until softened. With the mixer going, beat in 1 pound sugar until the mixture is light and fluffy, 3 to 5 minutes. Beat in the eggs, one at a time, until combined, then beat in the vanilla.
Step 4Beat in the dry ingredients, a spoonful at a time, just until incorporated. Be careful not to over-mix.
Step 5Fold in the cooked apples by hand. Spoon the mixture into the prepared cake pan and sprinkle over the remaining 3 tablespoons sugar.
Step 6Bake the cake in the center of the oven until the cake is risen and a rich golden brown on top, springs back when touched, and a toothpick inserted in the center comes out clean, about 1 1/2 hours. Check the cake after 1 hour; if it browns too quickly, loosely tent the top with a piece of foil.
Step 7Remove the pan to a rack. Cool for 15 minutes before removing the cake from the pan.