Preheat oven to 350 degrees F. Grease a 9×13 baking pan with cooking spray and set aside.
In a small skillet, melt 2 tablespoons of the butter over medium-high heat until the butter starts to bubble.
Add the peeled and chopped apples, 2 tablespoons of brown sugar, and ½ teaspoon pumpkin pie spice and cook, tossing occasionally, until the apples start to soften and the sugar mixture thickens, about 3-5 minutes. Remove from heat and set aside.
In a large mixing bowl add the remaining 1 cup of butter, ¾ cup brown sugar, and granulated sugar, and beat until light and fluffy (about 3 minutes), scraping the sides and bottom of the bowl as you go.
Add the eggs, one at a time, mixing after each addition. Stir in vanilla.
In another mixing bowl whisk together the flour, baking powder, ¾ teaspoon pumpkin pie spice, and salt.
Add about ⅓ of the flour mixture to the creamed butter/sugar mixture and stir until incorporated.
Add half of the buttermilk and stir. Repeat with another addition of flour, the rest of the buttermilk, and ending with the final addition of flour.
Add the cooked apple mixture to the batter and fold-in gently. Spread the batter into the prepared pan.
Bake for 35-43 minutes or until the cake is golden brown on top and a toothpick inserted into the center comes out clean. Remove from oven and allow to cool completely.
While the cake is cooling, make the frosting: Beat the cream cheese until smooth.
Add butter and cream together until smooth. Add the brown sugar and beat for about 5 minutes, or until very light and fluffy.
Mix in vanilla. Spread frosting evenly over cooled cake. Refrigerate leftovers.
