Beat butter at medium speed of an electric mixer until creamy. Gradually add 1 cup sugar, beating well. Add eggs, sour cream, and vanilla; beat well.
Combine flour, baking powder, soda, 3/4 teaspoon nutmeg, and salt; stir well. Gradually add to butter mixture, beating until blended. Cover and chill dough at least 3 hours.
Combine 1/3 cup sugar and remaining 1/4 teaspoon nutmeg; stir well. Shape dough into 1" balls. Place 2" apart on lightly greased cookie sheets. Grease bottom of a glass. Dip glass in sugar mixture, and press each ball flat.
Bake at 375° for 8 minutes or until edges are lightly browned. Remove cookies to wire racks immediately to cool.