Beat the butter and sugar until light and fluffy, about 2 minutes. Add the egg and vanilla, then mix until combined. Whisk flour, baking powder, and salt together, then add to the butter mixture in two additions, mixing just until the dough comes together. Divide dough in half, flatten into disks, wrap, and chill at least 1 hour.

Preheat oven to 350°F (175°C). Roll out one disk of dough on a floured surface to 1/4-inch thick. Cut with cookie cutters and place on parchment-lined baking sheets.

Whisk egg yolks and water together. Divide among small bowls and stir in gel food coloring to your preferred shades. The paint should be the consistency of thin syrup.

Paint designs onto the unbaked cookies using food-safe brushes, keeping coats thin. Bake for 8 to 10 minutes, rotating pans halfway through, until edges are just golden.

Cool cookies on the pans for 2 minutes, then transfer to a wire rack to cool completely. Arrange and serve.