Peel the apples, cut in half, remove the cores, then dice into small cubes about 1/4 inch. In a medium bowl, toss the diced apples with granulated sugar, brown sugar, ground cinnamon, ground nutmeg, lemon juice, and cornstarch until evenly coated. Let sit at room temperature while making the biscuit dough.

In a large mixing bowl, whisk together all-purpose flour, granulated sugar, baking powder, and salt until evenly distributed.

Add the cubed cold butter to the flour mixture and use a pastry cutter or two forks to work the butter into the flour until the mixture resembles coarse breadcrumbs with some pea-sized butter pieces visible. Work quickly and keep everything cold.

Pour the whole milk and vanilla extract into the flour mixture and stir gently with a wooden spoon or spatula until a shaggy dough just comes together with no dry flour remaining. Do not overmix.

Turn dough out onto a lightly floured surface and pat into a 1/2-inch thick rectangle. Using a 3-inch round biscuit cutter or a glass, cut out 12 rounds, gently re-rolling scraps as needed.

Place 6 biscuit rounds on a parchment-lined baking sheet, spacing about 2 inches apart. Add a heaping tablespoon of apple filling to the center of each biscuit, then top with another biscuit round. Gently press the edges together to seal.

Brush the top of each assembled biscuit lightly with melted butter, then sprinkle with coarse sugar.

Refrigerate the assembled biscuits for at least 10 minutes, preferably 20 minutes, to chill before baking. Alternatively, freeze them for up to 3 months and bake from frozen with an additional 5 minutes baking time.

Preheat oven to 400 degrees Fahrenheit. Bake chilled biscuits for 18 to 22 minutes until golden brown and a toothpick inserted into the biscuit (not the filling) comes out clean. If bottoms are not browning, move baking sheet to a lower oven rack for last 5 minutes.

Transfer baked biscuits to a cooling rack and let cool for 5 to 10 minutes before serving to allow the filling to set slightly. Best served warm.