Preheat oven to 350F degrees. Spray an 8-inch casserole dish with non stick cooking spray and set aside.
Make the cobbler batter: Combine the flour, baking powder, salt, granulated sugar, brown sugar and pumpkin pie spice in a medium mixing bowl. In a separate large bowl, whisk together the pumpkin puree, evaporated milk, eggs, melted butter and vanilla. Add the dry ingredients to the mixture of wet ingredients and whisk until just combined and all of the lumps are gone. Pour into the prepared baking dish.
1 cup all-purpose flour, 2 teaspoons baking powder, 1/2 teaspoon salt, 1/2 cup granulated sugar, 1/2 cup brown sugar, 2 teaspoons pumpkin pie spice, 2 eggs, 1/2 cup pumpkin puree, 3/4 cup evaporated milk, 1/4 cup unsalted butter, 1 1/2 teaspoons vanilla extract
Make the snickerdoodle topping: Cream the butter and sugar with a stand mixer or handheld mixer on high for 2-3 minutes. Add the egg, vanilla, baking soda, cream of tartar and salt and beat for another 1-2 minutes, scraping down the sides as needed. Add the flour and beat until combined.
1/2 cup unsalted butter, 1/2 granulated sugar, 1 egg, 1 teaspoon vanilla extract, 1/2 teaspoon baking soda, 1/2 teaspoon cream of tartar, 1/2 teaspoon salt, 1 cup all purpose flour
Top the cobbler with dough: Use small spoonfuls to scoop the snickerdoodle cookie on top of the batter, until it's almost completely covered in dough. It's ok if some cobbler is showing.
Sprinkle with cinnamon sugar: Mix the cinnamon sugar in a small bowl. Use a spoon to sprinkle it on top of the snickerdoodle cobbler.
1/4 cup Cinnamon Sugar Topping: 1/4 cup sugar + 1 1/2 tsp cinnamon
Bake: Bake the cobbler in the preheated oven for 50-60 minutes, or until a toothpick inserted comes our clean with a few crumbs. Start checking it about 15 minutes before it's done and tent it with foil if it's starting to look too brown on top. Serve it warm with of vanilla ice cream.