Preheat the oven to 350 degrees F. Line a 12-cup standard muffin tin with paper liners and set aside.

In the bowl of an electric mixer fitted with a paddle attachment, beat the cream cheese, 1/3 cup sugar, and 1/2 teaspoon pumpkin pie spice on medium speed until light and fluffy, about 2-3 minutes. Set aside.

In a large bowl, combine all the dry ingredients: flour, pumpkin pie spice, baking powder, cinnamon, baking soda, nutmeg, and salt.

In a large glass measuring cup or another bowl, whisk together the pumpkin puree, both sugars, vegetable oil, and eggs.

Pour the pumpkin mixture over the dry ingredients and stir with a rubber spatula until just moist.

Scoop a spoonful of batter into the muffin tray. Drop 2 teaspoons of the cream cheese filling into the center of each cup. Top with remaining batter to cover the filling completely.

Bake in the oven for 15-18 minutes, or until a tester inserted in the center comes out clean. Remove from the oven and cool completely on a wire rack before frosting.

In the bowl of an electric mixer fitted with a paddle attachment, beat the butter and confectioners’ sugar on medium speed until light and fluffy, about 1-2 minutes.

With the mixer on low speed, add the milk, vanilla, and 1 teaspoon pumpkin pie spice, beating until incorporated.

Increase the speed to medium-high and beat until frosted mixture is light and fluffy, about 1-2 minutes.

Use a small offset spatula or a pastry bag fitted with decorative tip #807 to frost the cupcakes. You can sprinkle graham cracker crumbs on top for extra style if desired.