Prepare the oven and pan: Preheat the oven to 350°F (175°C). Thoroughly grease a 10 to 12-cup Bundt pan, making sure to coat every groove. Lightly dust with flour and tap out the excess.
Combine the dry ingredients: Whisk together the flour, baking powder, baking soda, pumpkin pie spice, cinnamon, and salt in a medium bowl.
Cream the butter and sugars: In a large bowl, beat the softened butter, granulated sugar, and brown sugar until light and fluffy, about 2 to 3 minutes.
Add the eggs: Beat in the eggs one at a time, mixing well after each addition. Mix in the vanilla extract.
Add the pumpkin: Stir in the pumpkin puree until evenly incorporated.
Finish the batter: Add the dry ingredients in three additions, alternating with the buttermilk. Mix just until combined. Do not overmix.
Fill the pan: Spoon the batter evenly into the prepared Bundt pan. Gently tap the pan once or twice against the counter to settle the batter.
Bake: Bake for 50 to 60 minutes, or until a toothpick inserted into the thickest part comes out clean or with a few moist crumbs.
Cool: Let the cake cool in the pan for 10 to 15 minutes. Carefully invert it onto a wire rack and allow it to cool completely.
Brown the butter: Melt the butter in a small saucepan over medium heat. Continue cooking until golden-brown flecks appear and the butter smells toasted and nutty. Remove from the heat promptly.
Make the glaze: Let the browned butter cool slightly. Whisk it with powdered sugar, vanilla, salt, and 2 tablespoons of milk or cream. Add more liquid gradually if needed.
Glaze the cake: Drizzle the glaze over the completely cooled Bundt cake, allowing it to flow naturally over the ridges. Let the glaze set for about 15 to 20 minutes before slicing.
