Preheat oven to 350°. Bake almonds in a single layer in a shallow pan 6 minutes or until toasted and fragrant, stirring halfway through. Cool completely (about 20 minutes). Reduce oven temperature to 325°.
Process almonds in a food processor 30 seconds or until finely ground.
Beat butter at medium speed with a heavy-duty electric stand mixer until creamy. Gradually add vanilla and 1 cup powdered sugar, beating well. (Dough will be crumbly.)
Combine flour, salt, and almonds; gradually add to butter mixture, beating until blended.
Shape dough into 3/4-inch balls, and place 2 inches apart on parchment paper-lined baking sheets.
Bake at 325° for 12 to 15 minutes or until edges are lightly browned. Cool on baking sheets 2 minutes. Transfer to wire racks, and cool 10 minutes. Roll cookies in 1/2 cup powdered sugar.