Make the cookies: Whisk together the flour, baking powder and salt in a medium bowl. Beat the butter and granulated sugar in a large bowl with an electric mixer on medium-high speed until light and fluffy, 3 to 5 minutes. Beat in the vanilla and egg until incorporated. Reduce the mixer speed to low; add the flour mixture and beat until just combined.
Transfer 1 tablespoon dough to a small bowl and add 1 drop orange food coloring. Use a small spoon to mix until an even vibrant orange; set aside. Add 1/2 teaspoon yellow food coloring to the dough left in the bowl and mix on low until an even vibrant yellow. Refrigerate both doughs on a baking sheet, uncovered, until just firm, about 20 minutes.
Roll the yellow dough into an 8-inch cylinder, about 1 1/2 inches wide. Flatten the top of the log slightly to form an oval or egg-shaped log. Roll the orange dough into an 8-inch rope. Press into a triangular shape by flattening the sides (a ruler is helpful for this). Freeze both doughs on a baking sheet, uncovered, until hard, about 20 minutes.
Slice lengthwise through the yellow log, cutting off the top third and making 2 half-moon logs, one larger and one smaller. Make a small slit, about 1/8 inch deep, down the length of the larger log on the center flat side. Gently insert one of the pointed sides of the orange dough into the slit, being careful not to flatten out the triangle. Place the smaller log on top and press together to seal and re-form into an egg-shaped log, making sure the edges are smooth. Freeze until solid, about 1 hour.
Position oven racks in the upper and lower thirds of the oven and preheat to 350 degrees F. Line 2 baking sheets with parchment.
Cut 1/4 inch off each end of the log with a very sharp knife. Slice the cylinder into 24 cookies, each about 1/3 inch thick. Arrange the slices about 1 inch apart on the prepared baking sheets. Bake, rotating the pans halfway through, until crisp and just starting to turn brown on the bottom, 10 to 12 minutes. Let the cookies cool on the baking sheet for 10 minutes before transferring to a cooling rack to cool completely.
Make the icing: Whisk together the confectioners' sugar and meringue powder in a large bowl. Add 5 tablespoons water and beat with a mixer on medium-high speed until soft glossy peaks form, adding up to 1 more tablespoon water if necessary. Cover the bowl with a damp paper towel and plastic wrap until ready to use to prevent the icing from drying out. (Makes about 2 1/4 cups.)
When ready to ice the cookies, transfer about 1/2 cup of the icing to a resealable plastic bag and snip a small opening in one corner. Use this icing to pipe a thin border around the bottom half of each cookie and make an outline of a cracked eggshell about halfway up. Let set for a few minutes.
Thin the remaining icing with a few drops of water until it's the consistency of syrup. Transfer about 1 cup of the thinned icing to a resealable plastic bag. Divide the remaining thinned icing among 3 small bowls and tint each with a different color of pastel food coloring; transfer each color to a separate resealable plastic bag.
Snip a corner of the white icing bag and pipe a generous amount inside the icing border of each cookie. Using a small offset spatula or the back of a spoon, spread the icing to cover the cookie inside the border. Use the white icing to attach 2 mini chips for the eyes. Snip a corner of each pastel-tinted icing bag and use them to decorate the eggshells. Decorate with sprinkles or decorating sugar as desired. Let the icing dry completely before serving, about 30 minutes.
When measuring flour, we spoon it into a dry measuring cup and level off excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)
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