With an electric mixer, beat 2 cups sugar and butter until soft and creamy. Beat in milk, eggs and vanilla.
In a separate large bowl, stir together flour, baking powder and salt. Add to butter mixture in thirds, mixing well after each addition.
Divide dough into fourths, wrap each piece in plastic and chill, at least 2 hours or up to overnight. Mix remaining 1/4 cup sugar with cinnamon; cover and set aside.
Preheat oven to 350°F. Line a large rimmed baking sheet with parchment. Working with one fourth at a time on a lightly floured surface, roll out dough to a little less than 1/4 inch thick. Use a 4-inch, 5-point star-shaped cookie cutter to cut out cookies. Place stars 2 inches apart on cookie sheet; sprinkle with cinnamon-sugar. Bake until cookies spring back slightly when pressed in center, 10 to 12 minutes. Cool on pans on wire racks for 5 minutes; remove cookies to racks to cool completely.