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.
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.)
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.
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).
