1. Preheat oven to 375°. Beat butter at medium speed with an electric mixer until creamy. Gradually add 2 cups sugar, beating well. Add eggs, milk, and vanilla, beating well.
2. Combine flour, baking powder, and 2 tsp. cinnamon; gradually add to butter mixture, beating at low speed just until blended. (If desired, store dough in an airtight container in refrigerator up to 1 week.)
3. Combine 3 Tbsp. sugar and 1 1/2 Tbsp. cinnamon in a small bowl. Roll dough into 1 1/4-inch balls, and roll in sugar mixture. Place on ungreased baking sheets, and flatten slightly.
4. Bake at 375° for 11 to 13 minutes or until lightly browned. Cool on baking sheets 5 minutes. Transfer to wire racks, and cool completely (about 30 minutes).