Beat butter and 2 cups sugar with an electric mixer in a large bowl until creamy. Add eggs and vanilla; beat until smooth.
Sift flour, pumpkin pie spice, baking powder, and salt together in a bowl. Add flour mixture to butter mixture and beat until flour is completely incorporated. Cover dough with plastic wrap and refrigerate until chilled, at least 1 hour.
Preheat oven to 375 degrees F (190 degrees C). Spray baking sheets with cooking spray.
Pour 1/4 cup sugar into a shallow bowl.
Drop spoonfuls of dough 2 inches apart onto prepared baking sheets. Moisten the bottom of a glass with water and dip the glass in sugar. Gently flatten each drop of cookie dough with the bottom of the sugared glass.
Bake cookies in the preheated oven until set, 5 to 7 minutes.