Cream butter; beat in sugar gradually. Add eggs, milk, and vanilla extract; stir to blend. Combine and sift flour, baking powder, and salt; add gradually to creamed mixture, mixing thoroughly. Cover and refrigerate for 4 hours or overnight. Shape dough into 3/4-inch balls. Place 2" apart on greased baking sheet. Flatten with bottom of glass that's been greased and dipped in granulated sugar. Bake at 375° for 8-10 minutes or until edges are lightly browned. Remove to racks immediately to cool.
Makes about 3 dozen.
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