In a small skillet, melt 3 tablespoons of butter over medium heat. Add 1 ⅓ cups chopped pecans and toast for 4–5 minutes, stirring frequently, until golden and fragrant. Set aside to cool.

Preheat the oven to 350°F (175°C). Grease and flour two 9-inches round cake pans. In a medium bowl, whisk together 2 cups flour, 1 ½ teaspoons baking powder, and ¼ teaspoon salt.

In a large bowl, beat ⅔ cup softened butter with 1 ½ cups granulated sugar using an electric mixer until light and fluffy, about 3–4 minutes. Add eggs one at a time, beating well after each addition. Stir in 1 ½ teaspoons vanilla extract.

Alternately add the flour mixture and 1 cup milk to the butter mixture, beginning and ending with the flour mixture. Mix until just combined. Fold in the toasted pecans.

Divide the batter evenly between the prepared cake pans. Bake for 30–35 minutes or until a toothpick inserted in the center comes out clean. Let cakes cool in pans for 10 minutes, then transfer to a wire rack to cool completely.

In a saucepan, melt 1 ½ cups butter with ⅓ cup light brown sugar over medium heat until golden and slightly nutty. Let cool slightly. In a large bowl, beat 6 oz softened cream cheese, 1 ½ teaspoons vanilla extract, 1 tablespoon heavy cream, and ¼ teaspoon salt until smooth. Gradually add 4 ½ cups powdered sugar and the brown butter mixture, mixing until fluffy.

Place one cake layer on a serving plate. Spread a generous layer of icing over the top. Place the second cake layer on top and cover the entire cake with remaining icing, smoothing with a spatula. Optional: sprinkle extra toasted pecans on top for garnish.

Let the cake sit for 30 minutes before slicing for best flavor. Store leftovers in an airtight container in the refrigerator for up to 4 days.