Preheat oven to 350F and line a half-sheet pan with parchment paper.
Whisk together the almond meal, cornmeal, coconut flour, baking powder, whey, baking soda, salt, and sugar in a medium bowl. In a separate large bowl, whisk together the coconut oil, almond butter and honey until smooth, then whisk in 1 egg, the milk, vanilla extract, and almond extract. Pour all the dry ingredients into the wet and stir with a wooden spoon until incorporated; let the batter rest for 3 minutes.
Turn the batter out onto the prepared baking sheet and spread it into a log about 12 inches long by 2 1/2 inches wide; bake 15 minutes. Remove the cookie log from the oven and let it cool 10 minutes, then crumble it into a large bowl. Lightly beat the remaining 3 large eggs, then stir the eggs into the crumbled cookie. Shape the batter into a log about the same size as before and bake until golden, about 20 minutes. Remove from oven and turn oven down to 325°F.
Cool the cookie log completely, then cut cross-wise into about 1/3 inch-thick slices. Arrange in a single layer on a baking sheet and bake until golden on each side, about 20 minutes per side, flipping once.
Cool the cookies completely, then serve with coffee.