Preheat oven to 350°F. Spread pecans on a baking sheet in a single layer. Toast for 8-10 minutes, stirring halfway through, until fragrant and slightly darker. Watch carefully to prevent burning. Let cool completely, then chop roughly.

Melt butter in a light-colored saucepan over medium heat. Continue cooking, swirling the pan occasionally, until butter turns golden brown and smells nutty, about 5-7 minutes. Watch closely as it goes from perfect to burned quickly. Pour into a bowl and let cool to room temperature.

Grease and flour two 9-inch round cake pans. In a large bowl, whisk together flour, baking powder, baking soda, and salt. In another large bowl, beat together cooled browned butter, granulated sugar, and brown sugar until fluffy, about 3 minutes. Add eggs one at a time, beating well after each. Mix in vanilla extract.

Alternate adding dry ingredients and buttermilk to the butter mixture in three additions, starting and ending with dry ingredients. Mix just until combined after each addition. Gently fold in chopped toasted pecans. Divide batter evenly between prepared pans. Smooth tops with a spatula.

Bake at 350°F for 25-30 minutes, until a toothpick inserted in the center comes out with just a few moist crumbs. Let cool in pans for 10 minutes, then turn out onto wire racks to cool completely.

Beat softened cream cheese and butter together until fluffy, about 2 minutes. Gradually add powdered sugar, one cup at a time, beating between additions. Mix in vanilla extract. Add heavy cream one tablespoon at a time until you reach desired spreading consistency. Place one cake layer on serving plate. Spread about 1 cup of frosting on top. Place second layer on top. Frost top and sides with remaining frosting. Press extra toasted pecans around the sides if desired. Drizzle with caramel sauce if using. Refrigerate 30 minutes to set frosting before slicing.