Preheat your oven to 350°F (175°C).
In a large mixing bowl, combine the softened unsalted butter and powdered sugar. Cream together until light and fluffy, about 2-3 minutes.
Stir in the vanilla extract until well incorporated.
In a separate bowl, whisk together the all-purpose flour, salt, and baking powder.
Gradually add the dry mixture to the creamed butter and sugar. Mix until just combined.
Gently fold in the chopped walnuts with a spatula.
Drop rounded balls of dough onto a lined baking sheet, spacing them about 2 inches apart.
Bake in the preheated oven for 12-15 minutes, until the edges are lightly golden.
Let the cookies cool on the baking sheet for about 5 minutes, then transfer to a cooling rack and dust with extra powdered sugar.