Adjust the rack to the middle position (or the best position in your oven for baking; mine is NOT the middle position) and preheat the oven to 350. Grease a 9×13″ baking pan 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 apples, 2 tablespoons of brown sugar, and 1/2 teaspoon pumpkin pie spice and sauté until the apples start to soften and the brown sugar/butter mixture becomes thick and syrupy, about 3-5 minutes. Remove from heat and set aside.

Whisk the flour, baking powder, 3/4 teaspoon pumpkin pie spice, and salt together in a medium bowl. In a large bowl or the bowl of a stand mixer fitted with the paddle attachment, beat the butter, brown sugar, and granulated sugar on medium high speed for about 3 minutes or until light and fluffy (scrape the bowl as necessary). Add eggs one at a time, beating until just combined after each addition. Reduce speed to medium and add 1/3 of the flour mixture, mixing until incorporated. Mix together the buttermilk and vanilla and then add 1/2 cup buttermilk to the flour/butter/sugar mixture. Repeat with another addition of flour, the rest of the milk, and ending with the final addition of flour. Add the apple mixture to the cake batter and fold gently. Spread the batter into the prepared pan.

Bake for 35-50 (I have a gas oven, so my times tend to be way off; I'm giving a lot of leeway here) 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, place 1/2 cup (that's 1 stick) of salted butter into a small saucepan and heat over medium, stirring frequently, until it starts to bubble. When it begins to bubble, reduce the heat to low. Don't go anywhere--things can go south quickly. Once the butter becomes very frothy, you'll start to notice a caramel-like smell--that means the butter is browning. When the butter is brown (and before it burns), remove it from heat.

In a large mixing bowl, combine 1/4 cup heavy cream, 1 tablespoon vanilla extract, the powdered sugar, and the melted butter and mix on high speed with a stand or electric mixer. Add additional heavy cream in order to reach the desired consistency.

When the cake is completely cool, spread the frosting over the cake and cut into squares. Makes 12-16 servings.