Brown-butter:

• Prep the brown butter ahead of time as it needs time to cool and re-solidify before it can be used for the frosting. 
• In a small saucepan, melt butter on low-medium heat. As the butter melts, you should see big fast bubbles and hear the butter crackle. Give the pan a swirl every 30 seconds or so to ensure the butter melts evenly. After about 5-7 minutes, the bubbles will become small (almost like foam), the crackling sound will stop, and the browning process will begin. Pay close attention; you don’t want to burn the butter. It will gradually change to an amber color. At this point, remove from heat, pour into a bowl, and refrigerate until solid.

Pumpkin Cupcakes:

• Preheat oven to 350°F (176° C). Line 12 cupcake tins and set them aside. 
• Whisk together dry ingredients (flour, baking powder, baking soda, pumpkin spice, and salt) in a medium bowl. Set aside. 
• In another bowl, whisk together all wet ingredients (pumpkin puree, eggs, and vanilla) until combined. Set aside. 
• In a bowl of a stand mixer fitted with a paddle attachment, cream together butter and both sugars on medium speed for 2-3 minutes. The mixture should look fluffy and pale in color. 
• At low speed, alternate between dry and wet ingredients in 3 increments, starting and ending with the dry ingredients to prevent curdling. 
• Evenly fill cupcake tins with batter. The batter should fill halfway up the liner. 
• Bake at 350°F (176° C) for 16 - 18 minutes.
• Check for doneness by inserting a toothpick into the middle of the cupcake. Your cupcakes are done if a few moist crumbs come out. If not, keep baking in 1-2 minute increments.
• Once done, let them rest in the pan for 5 minutes before transferring them to a cooling rack.

Brown-butter Cream Cheese Frosting:

• In a bowl of a stand mixer fitted with a paddle attachment, on medium-low speed cream brown butter for 15-20 seconds. Add in cream cheese and cream together until well incorporated. The mixture should lighten in color and become fluffy. 
• Add in half the powder sugar and mix until combined. Scrape the sides of the bowl before adding in more sugar. Add in the remaining sugar, salt, and vanilla and mix until well combined.