Preheat oven to 350°F (177°C). Line a 12-cup muffin pan with paper liners.
Tip: Make the brown butter for the frosting now if you want to assemble the cupcakes on the same day.
In a large bowl combine sugars, oil, vanilla extract, eggs, pumpkin puree and milk. Mix until combined.
In a small bowl (or large measuring cup) combine flour, baking powder, baking soda, spices, and salt.
Add dry ingredients to wet ingredients and stir until just combined. Don't overmix!
Spoon the batter into muffin cups - fill only 1/2 full and bake for 20 to 25 minutes, or until a skewer inserted in the center comes out clean with only a few crumbs attached.
Let the cupcakes cool in the pan for 10 minutes then transfer to a cooling rack to cool completely before frosting.
Brown the butter for the frosting: Slice 1/4 cup butter up into pieces and place in a light colored skillet. Melt it over medium-low heat, stirring occasionally, until lightly browned. Lightly browned bits will begin to form at the bottom of the pan and it will have a nutty aroma. This takes about 5-8 minutes. Once browned pour the butter into a heatproof bowl and refrigerate until solid.
Make the frosting: In a large bowl using a handheld or stand mixer fitted with a paddle attachment beat the remaining un-browned butter on medium speed until smooth and creamy, about 30 seconds.
Add the cooled brown butter and beat until combined.
Then add the powdered sugar and vanilla extract, beat on low speed for 30 seconds until combined.
Gradually add the buttermilk, one tablespoon at a time, until spreadable. Beat for 1 more minute at high speed.
Frost the cooled cupcakes however you'd like. I used a Wilton 1A round piping tip for the pictured cupcakes. Top with salted caramel and chopped pecans, if desired.