1. Preheat oven to 350°.
2. Melt butter in a large skillet over medium-low heat; cook 6 minutes or until dark brown. Pour butter into a large bowl; let stand 5 minutes. Add granulated sugar and 1/2 teaspoon vanilla; beat with a mixer at medium speed until well blended (about 2 minutes). Add egg yolks, and beat at medium speed until well blended (about 1 minute).
3. Weigh or lightly spoon flour into dry measuring cups; level with a knife. Combine flour, salt, and baking powder; stir with a whisk. Add flour mixture to butter mixture; beat at low speed just until combined. Turn dough out onto a sheet of wax paper; knead gently 7 times. Roll dough to a 1/4-inch thickness. Cut with a 2 1/2-inch star-shaped cookie cutter into 32 cookies; reroll scraps as necessary. Arrange cookies 1 inch apart on baking sheets lined with parchment paper. Bake, 1 batch at a time, at 350° for 10 minutes or until edges are lightly browned. Cool cookies completely on wire racks.
4. Combine powdered sugar, half-and-half, and 1/4 teaspoon vanilla extract, stirring with a whisk until icing is smooth. Spoon about 3/4 teaspoon icing onto each cookie; spread to edges. While icing is wet, sprinkle each cookie with 1/2 teaspoon pearlized sugar. Dry on wire racks.