Step 1: Preheat your oven to 350°F (175°C). Grease and flour two 9-inch round cake pans or line with parchment paper.
Step 2: In a medium bowl, whisk together the all-purpose flour, baking powder, and salt. Set aside.
Step 3: In a large bowl, cream together the softened unsalted butter (first amount) and granulated sugar with an electric mixer until light and fluffy, about 3-5 minutes. Beat in the eggs one at a time, ensuring each is fully incorporated before adding the next. Stir in 2 teaspoons of pure vanilla extract.
Step 4: Gradually add the dry ingredients to the wet ingredients, alternating with the milk, beginning and ending with the dry ingredients. Mix until just combined; do not overmix. Gently fold in the toasted and chopped walnuts.
Step 5: Divide the batter evenly between the prepared cake pans. Bake for 25-30 minutes, or until a wooden skewer inserted into the center comes out clean. Let the cakes cool in the pans for 10 minutes before inverting them onto a wire rack to cool completely.
Step 6: For the frosting, in a large bowl, beat the softened unsalted butter (second amount) with an electric mixer on medium speed until creamy, about 2 minutes.
Step 7: Gradually add the powdered sugar, one cup at a time, beating well after each addition until smooth. Add 1 teaspoon of pure vanilla extract and 3-4 tablespoons of heavy cream (or milk), and beat on high speed until light and fluffy, about 3-5 minutes. Adjust consistency with more cream or powdered sugar if needed.
Step 8: Once the cake layers are completely cool, place one layer on a serving plate or cake stand. Spread about one-third of the creamy butter frosting evenly over the top. Place the second cake layer on top and spread with another third of the frosting.
Step 9: Use the remaining frosting to cover the sides and top of the cake. Garnish with additional chopped walnuts, if desired.
Step 10: Allow the cake to set in the refrigerator for at least 30 minutes before slicing and serving.