Heat oven to 350°F. Line two baking sheets with parchment; set aside. In a bowl whisk together cake flour, all-purpose flour, baking powder and salt. In another bowl beat together butter, sugar and 1 teaspoon vanilla until fluffy, about 3 min. Beat in the eggs and egg yolks one at a time. Reduce speed, add the flour mixture and stir until just combined. Scrape sides of bowl to evenly mix batter.
Transfer dough to a ziplock bag and sip a corner for piping ¾-inch mounds, or spoon batter by heaping teaspoon onto baking sheets, 1 inch apart. Freeze for 10 min. Bake until cooked but not browned, 8 to 9 min. Cool 5 min, then transfer to a wire rack.
Make Glaze: Combine confectioners' sugar, corn syrup, water and remaining 1 teaspoon vanilla until smooth. Keep half the glaze un-tinted. Divide remaining glaze between two bowls and tint blue and pink.
Turn the cookies bottom side up. Spread or pipe half of each bottom with the colored glaze and half with the white glaze. Allow glaze to set, about 30 min. Store cookies airtight for up to 3 days.