Preheat oven to 350 degrees Fahrenheit. Line a 12-cup muffin tin with paper liners.
Melt butter in a large microwave-safe bowl. Immediately whisk in pumpkin pie spice and cinnamon. Set aside to cool completely.
In a separate bowl, whisk flour, both sugars, baking soda, baking powder, and salt together.
Once butter is cool, stir in pumpkin puree. Add eggs and vanilla and whisk to combine. Stir in milk.
Add dry ingredients to wet and fold gently until just combined. Do not overmix and do not use an electric mixer.
Divide batter evenly among lined cups, filling each two-thirds to three-quarters full.
Bake 18 to 20 minutes until a toothpick comes out clean or with a few moist crumbs.
Cool in pan 5 to 7 minutes. Transfer to wire rack and cool completely.
For frosting: beat cream cheese and butter until smooth. Add brown sugar, vanilla, and salt and beat 30 seconds. Add powdered sugar gradually on low speed. Add heavy cream if using and beat on high 30 seconds until silky.
Pipe or spread frosting over completely cooled cupcakes.