Preheat the oven to 350° F. Line your muffin tins with paper liners and set aside.
In a large bowl, combine flour, pumpkin pie spice, baking powder, cinnamon, baking soda, and salt.
In a large bowl, add in pumpkin puree, sugars, vegetable oil, vanilla extract, and eggs and whisk together. Add in flour mixture into the pumpkin puree mixture and gently mix with a rubber spatula until smooth and everything is combined.
Spoon the batter into the lined muffin tins evenly about 2/3 full. Put into the oven and bake for 15-18 minutes. Remove from oven and cool completely before frosting.
To make the frosting, melt the butter in a small saucepan over medium heat. Once melted, add the light brown sugar and 2 Tablespoons of heavy cream. Whisk constantly until sugar is dissolved. Add 1/4 tsp salt and allow the mixture to bubble for about 2 minutes, whisking about every 30 seconds. Remove from heat, pour into a heat proof mixing bowl or stand mixer bowl and cool for 30 minutes.
Using a stand or hand mixer with a whish attachment, beat in 2 cups powdered sugar and 3 more Tablespoons of heavy cream. Gently whisk in 1/2 cup more powdered sugar. If you like the consistency, keep it as is, but if you would like to thin the frosting a little, add 1 more Tablespoon of heavy cream. Taste the frosting, and if you'd like a little more salt, add 1/4 tsp and whisk one more time.
Pipe or spread frosting on each cooled cupcake. To garnish, you can drizzle caramel sauce, sprinkle coarse sea salt, and add a pumpkin candy on top. Enjoy!