Begin by preheating your oven to 350 degrees F. Line two muffin pans with paper liners; set aside. In a skillet, heat 3 tablespoons of butter over medium heat. Add the chopped pecans and cook 5-6 minutes until toasted. Allow the pecans to cool.
In the meantime, in a medium bowl, whisk together the flour, baking powder, and salt. Set aside.
Then, with a mixer, cream together 1 cup butter with the sugar until light and fluffy. Add the eggs one at a time, beating well after each addition. Scrape the bowl down when needed. Beat in the vanilla. Mix in the dry ingredients, alternating with the milk. Beat until just combined. Fold in 2 cups of the pecans and save the remainder for the frosting.
Scoop the batter evenly into the prepared muffin tins. Bake for 18-20 minutes or until a toothpick inserted near the center of a cupcake comes out clean. Remove the cupcakes from the pan and allow to cool on a wire rack.
Meanwhile, prepare the Butter Pecan Frosting. With a mixer, beat the cream cheese and butter together 5-6 minutes until light and fluffy. Slowly add the confectioners' sugar, 1 cup at a time, mixing in between. Beat in the vanilla and salt. Add enough milk to achieve a smooth consistency. Fold in the remaining 3/4 cup pecans. Spread the frosting on the cupcakes with a spatula and top with a pecan half.