Place the 8 tablespoons of unsalted butter in a light-colored saucepan over medium heat. Cook, stirring frequently, until it melts, foams, and starts to brown. The butter will take on a nutty aroma and turn golden brown with specks. Immediately remove from heat and pour into a heatproof bowl to cool slightly.

Preheat your oven to 350°F (175°C). Grease your cake pan (8-inch round or 9×9-inch square) and line the bottom with parchment paper for easy release.

In a large bowl, whisk together the flour, baking powder, baking soda, salt, nutmeg, and the vanilla pudding mix. Set aside.

In another bowl, beat the cooled browned butter and brown sugar together until smooth. Add in the eggs and egg white, mixing well. Stir in the buttermilk, heavy cream, vanilla extract, and almond extract. Mix until fully combined.

Add the dry ingredients to the wet mixture in two batches, stirring gently until just combined. Do not over mix the batter should be smooth but not overworked.

Pour the batter into your prepared pan and smooth the top. Bake for 30–35 minutes, or until a toothpick inserted into the center comes out clean or with a few moist crumbs. Remove from oven and let cool in the pan for 10 minutes before turning out onto a wire rack to cool completely.

Brown the ¾ cup butter as you did before, then let it cool slightly. In a bowl, beat the browned butter with powdered sugar, 2 tablespoons of heavy cream, vanilla, and a pinch of salt. Adjust consistency with more cream if needed. Beat until light and fluffy.

Once the cake is fully cooled, spread the brown butter frosting evenly over the top. Slice and serve. Enjoy the rich, nutty flavor of browned butter paired with the moist, tender crumb of this unique cake.