Preheat your oven to 350°F (175°C). Lightly grease a 10-inch cast iron skillet with butter or cooking spray.
In a medium bowl, combine the diced apples with the 2 tablespoons of sugar, 1 teaspoon cinnamon, and ¼ teaspoon nutmeg. Toss well to coat the apples evenly.
In a large bowl, whisk together the melted butter and brown sugar until smooth and no sugar lumps remain (about 2 minutes of vigorous whisking).
Add the eggs one at a time, whisking well after each addition, then stir in the vanilla extract until combined.
In a separate bowl, whisk together the flour, baking powder, salt, cinnamon, and nutmeg.
Gradually add the dry ingredients to your wet ingredients, stirring just until combined. Don't overmix.
Gently fold about 2/3 of your spiced apple mixture into the batter, reserving the rest for topping.
Pour the batter into your prepared skillet, spreading it evenly to the edges.
Arrange the remaining apple pieces on top, then sprinkle with chopped pecans and turbinado sugar if using.
Bake in the preheated oven for 35-40 minutes, or until the edges are set and crispy while the center is just barely set. A toothpick inserted 2 inches from the edge should come out mostly clean with a few moist crumbs.
Allow the skillet apple brownie to cool for at least 15 minutes before serving.