Combine butter, sugar, brown sugar, egg yolks and vanilla in bowl; beat at medium speed until creamy. Add flour, baking powder and salt; beat at low speed until well mixed.
Divide dough in half. Shape each half into a ball; flatten slightly. Wrap each in plastic food wrap; refrigerate at least 2 hours until firm.
Cut candies in half crosswise to make 48 pieces; set aside.
Heat oven to 350°F.
Roll out dough, one-half at a time, on lightly floured surface (keeping remaining dough refrigerated), to 1/4-inch thickness. Cut with 2-inch round cookie cutter. Place half of cookies, 4 inches apart, onto ungreased cookie sheets.
Place egg white and 1 tablespoon water in bowl; beat with whisk until frothy. Press 1 lollipop stick into middle of each cookie on cookie sheet. Top with 1 piece candy. Brush egg white mixture over 1 side of remaining cookies; place over candy, egg wash-side down. Press dough gently around candy; crimp outer edges together to seal, using tines of fork.
Bake 10-13 minutes or until edges are just beginning to brown. Using spatula, remove to cooling racks. Cool completely.
Combine powdered sugar, corn syrup, 4 teaspoons water and almond flavoring in bowl; beat at medium speed until well mixed. Spread glaze over cookies. Decorate with decorator sugars, sprinkles or candies. Let stand until glaze is set.