In a large bowl, using an electric mixer, beat the butter on high speed until fluffy and pale yellow. Add 1/2 cup of the confectioners' sugar and continue beating until light and fluffy. Reduce the speed to low, add the vanilla and salt, and beat until blended.
Over a sheet of parchment paper, sift together the flour and cinnamon. Add the flour mixture to the butter mixture and beat on low speed just until blended. Stir in the almonds. Cover and refrigerate until the dough is chilled and is no longer sticky to the touch, about 15 minutes.
Sift the remaining 3/4 cup confectioners' sugar into a shallow bowl.
Shape the dough into 1-inch balls. Place each ball about 1 inch apart onto two parchment-lined baking sheets.
Bake until the cookies are just golden on the bottom, 10 to 12 minutes. Transfer the baking sheets to wire racks and let cool for 5 minutes, then remove the cookies one at a time and roll them in the confectioners' sugar. Allow the cookies to cool completely on wire racks.