Preheat the oven to 375°F. Grease a 12-cup muffin pan or line with paper liners. Set aside.
In a small saucepan over medium heat, melt the butter. Continue cooking, letting it swirl a bit, until it turns golden brown with little brown bits at the bottom (about 3-5 minutes). It should smell nutty. Remove from heat and let cool a little.
In a medium bowl, whisk together flour, pumpkin pie spice, baking powder, baking soda, and salt.
In a separate larger bowl, whisk together the sweet potato and browned butter until it’s nice and smooth.
Whisk in both sugars until combined and glossy.
Next, whisk in the eggs, bourbon, and vanilla.
Finally, fold the dry ingredients into the wet, but don’t overmix. Just until combined.
Scoop about ¼ cup batter into each muffin cup, filling about ¾ full.
Bake for 20-25 minutes, or until the muffin tops are set or until a toothpick inserted into the center comes out with a few moist crumbs. Cool for just 10 minutes, then remove from the pan.