Heat oven to 325°F. In large bowl, beat 1/2 cup powdered sugar, the butter and vanilla with electric mixer on medium speed until light and fluffy. On low speed, beat in flour, almonds and salt until dough forms.
Shape dough into 1-inch balls. On ungreased cookie sheets, place balls 1 inch apart.
Bake 13 to 17 minutes or until set but not brown. Immediately remove from cookie sheets to cooling racks. Cool slightly, about 10 minutes.
Place 3/4 cup powdered sugar in small bowl. Roll cookies in powdered sugar. Cool completely, about 15 minutes. Roll in powdered sugar again. Cookies can be placed in an airtight container and freeze up to 3 weeks. Before serving, thaw the cookies and reroll them in powdered sugar.