Preheat the oven to 450°F.

Make the apple filling. Melt 3 tablespoons salted butter in a skillet over medium heat. Add the diced apples, brown sugar, cinnamon, and nutmeg. Cook for 4–6 minutes, stirring occasionally, until the apples begin to soften and the liquid has reduced to a thick, sticky coating.

Remove the apples from the heat and stir in 1 teaspoon vanilla extract. Set aside to cool slightly.

Add the sliced stick of butter to a 9×9-inch baking dish. Place the dish in the oven just until the butter is melted, then remove from the oven.

Place the baking dish on a foil- or parchment-lined sheet pan to catch any butter that may bubble over during baking.

In a large bowl, whisk together the flour, baking powder, kosher salt, granulated sugar, and cinnamon.

In a separate bowl or large measuring cup, combine the buttermilk, 2 tablespoons melted butter, and 1 teaspoon vanilla.

Pour the wet ingredients into the dry ingredients and stir just until combined -- DO NOT OVER-MIX! Gently fold in the cooked apple mixture.

Spoon the biscuit dough into the baking dish directly over the melted butter. Gently spread the dough evenly to the edges.

Score the dough into 9 biscuits with a knife. Generously sprinkle the top with turbinado sugar.

Bake at 450°F for 30–35 minutes, or until the biscuits are cooked through and deeply golden brown. Loosely tent the baking dish with foil around the 27-minute mark if the tops are sufficiently browned before the centers are finished baking.

Let cool for about 10 minutes before serving. Serve warm as-is or topped with salted butter and maple syrup.