Preheat oven to 350 degrees F. Line a 12-cup muffin tin with paper liners; set aside.
CHEESECAKE FILLING: In the bowl of an electric mixer fitted with paddle attachment, beat cream cheese, sugar and pumpkin pie spice on medium speed until combined and creamy; set aside.
CUPCAKES: In a large bowl, combine flour, pumpkin pie spice, baking powder, cinnamon, baking soda, nutmeg and salt.
In another large bowl, stir/whisk together pumpkin puree, sugars, vegetable oil and eggs. Pour wet mixture over dry ingredients and stir until combined.
Scoop about 1/4 cup or slightly less batter into each muffin liner. Drop 2 teaspoons cream cheese filling into the center of each cup. Top with remaining batter to completely cover the filling. Place into oven and bake for about 18 minutes, or until a toothpick inserted in center comes out clean. Remove from oven and cool completely before frosting.
CREAM CHEESE FROSTING: In a large bowl, add cream cheese, butter and vanilla. Beat with an electric hand-mixer on medium speed until well combined. Gradually blend in powdered sugar. Frost cooled cupcakes then enjoy! (To pipe the frosting as pictured I used a Wilton 1A tip and piping bag.)
*This recipe can easily be doubled to make 24 cupcakes. *The frosting recipe makes a lot. You can cut it in half if you don't like a lot of frosting.