Preheat the oven to 350℉. Line a cast-iron skillet with parchment paper so that it covers all sides.
Brown the butter. Add the butter to a saucepan over medium-high heat. Let it melt and start to brown, stirring continuously for 5-7 minutes. Once golden brown, remove from the heat and pour into a large bowl. Set aside to cool, about 5-10 minutes.
½ cup browned butter
Meanwhile, prepare the pecan and cinnamon crumb topping. In a medium bowl, combine the flour, both sugars, cinnamon, nutmeg and butter. Mix with a fork or your hands until it resembles wet sand. Then, add the chopped pecans and mix in gently. Place into the refrigerator to chill while you make the apple cake.
1½ tsp ground cinnamon, 1½ cups all-purpose flour, ½ cup granulated sugar, ¼ tsp ground nutmeg, ½ cup unsalted butter, ¾ cup pecans, ½ cup brown sugar
In a large bowl, add the bananas and mash until no lumps remain. Then add the cooled browned butter and whisk together until combined. Then add the brown sugar and granulated sugar and whisk again. Add both eggs and the vanilla bean paste and whisk again.
½ cup browned butter, ¾ cup brown sugar, 2 eggs, 2 tsp vanilla bean paste, ¾ cup bananas, ¼ cup granulated sugar
Add in the applesauce and sour cream. Whisk together again.
¾ cup unsweetened applesauce, 1 cup sour cream
Add in the dry ingredients. Add in the flour, baking powder, baking soda, salt, and cinnamon. With a rubber spatula, mix until just combined and no flour streaks remain (do not overmix). Then fold in the chopped apples.
2⅔ cups all-purpose flour, 1½ tsp baking powder, 1 tsp baking soda, 1½ cups Honeycrisp apples, 2 tsp ground cinnamon, 1 tsp salt
Scoop the batter into the prepared skillet. Then sprinkle the pecan streusel all over the top.
Bake the cake in the oven for 50-60 minutes, until a knife comes out almost clean when inserted. Let cool for 5-10 minutes and eat warm.