Preheat your oven to 350°F (175°C). Grease and flour a 9×13-inch baking pan. In a medium-sized bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.
In a large mixing bowl, cream together the softened butter, granulated sugar, and brown sugar until light and fluffy. Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract.
Gradually add the dry ingredients to the wet ingredients, alternating with buttermilk. Begin and end with the dry ingredients. Mix until just combined.
Gently fold in the chopped walnuts and almonds until evenly distributed in the batter. Pour the batter into the prepared baking pan and spread it evenly.
Bake in the preheated oven for 40-45 minutes or until a toothpick inserted into the center comes out clean. Allow the cake to cool in the pan for about 10 minutes, then transfer it to a wire rack to cool completely.
You can frost or glaze the cake with your favorite frosting or glaze. Cream cheese frosting or a simple powdered sugar glaze work well.
Once the frosting or glaze has set, cut the cake into slices and serve. Enjoy your delicious cake with walnuts and almonds!