Preheat your oven to 350°F (175°C) and prepare a 9x13 inch baking pan.

In a medium bowl, whisk together flour, baking powder, baking soda, and salt.

In a stand mixer bowl, combine eggs and sugar, beat until light and fluffy. Mix in pumpkin puree, brown butter, buttermilk, and vanilla.

Gradually add the dry mixture to the wet mixture, mixing until just combined.

Pour the batter into prepared pan and bake for 30-35 minutes, checking for doneness.

For the frosting, melt butter in a skillet until golden brown, then mix with powdered sugar and milk until smooth.

Once the cake is cooled, frost it generously and add any desired decorations.

Slice and serve the cake with coffee or tea.