Beat butter and 1 1/2 cups sugar at low speed with an electric mixer until creamy. Add eggs, 1 at a time, beating until blended after each addition. Add milk, beating until blended. Add flour and next 6 ingredients, beating until blended. Cover and chill dough 8 hours.
Divide dough into fourths. Roll 1 portion to a 1/4-inch thickness on a lightly floured surface. Cut with a 1 1/2-inch round cookie cutter or very small glass. Repeat procedure with remaining portions.
Cook, in batches, on a hot, lightly greased electric griddle or lightly greased skillet over low heat, 2 to 3 minutes on each side or until golden. Remove to wire racks, and sprinkle warm tea cakes with powdered sugar. Cool slightly and serve, or cool completely and store in wax paper-lined airtight containers.
Note: Tea cakes may also be baked on lightly greased baking sheets at 350° for 10 minutes or until cookies are golden.