Preheat the oven to 425° with the rack in the middle.
Place a 10" cast-iron skillet on the rack and heat while you make the batter.
Make the Dutch Baby: Combine the eggs, flour, coconut milk, pumpkin purée, brown sugar, vanilla, pumpkin spice, and salt in a blender. Blend until smooth.
Remove the skillet from the oven and add 2 tablespoons butter, swirl to melt it.
Pour the batter in the hot pan and put the skillet back in the oven. Bake until the pancake is puffy and golden brown, 21 to 24 minutes.
While the pancake is baking, make the Caramelized Apples: Heat a medium cast iron skillet over medium heat. Melt the remaining 3 tablespoons butter, add the maple syrup, vanilla, salt and cinnamon. Add the apples and cook, stirring occasionally, until they soften, become fragrant and the sauce thickens. 10 to 12 minutes. Remove from heat but keep warm.
Serve the Dutch baby with powdered sugar, homemade whipped cream, topped with the apples and any juices left in the skillet.