Beat butter with a heavy-duty stand mixer on medium speed until creamy. Gradually add sugar, beating until light and fluffy. Add egg yolks, 1 at a time, beating until well incorporated after each addition. Beat in vanilla.

Stir together flour and salt in a medium bowl, and gradually add to butter mixture, beating at low speed just until blended. Shape dough into a 1-inch-thick disk. Wrap in plastic wrap, and chill until firm, about 1 hour.

Preheat oven to 300°F. Roll dough to 1/3-inch thickness on a lightly floured surface. Using a 2 1/2-inch round cookie cutter, cut out cookies. Place about 2 inches apart on a large parchment paper-lined baking sheet. Gather dough scraps, and reroll once to get a total of 18 cookies.

Using a small paring knife, cut 6 small triangular slits (3/4 inch long and 1/8 inch wide at the base) around perimeter of each cookie to mimic flower petals. Bake until golden brown around the edges, 20 to 22 minutes.

Cool cookies on baking sheet 5 minutes. Transfer to a wire rack to cool completely, about 30 minutes.

Prepare the Royal Icing: Combine powdered sugar, 1/4 cup water, meringue powder, and vanilla and almond extracts in the bowl of a stand mixer fitted with the paddle attachment. Beat on medium speed until blended, smooth, and stiff, scraping down sides as needed, about 1 minute (mixture should hold stiff peaks). Thin mixture as needed for recipe by gradually stirring in additional water 1/2 teaspoon at a time.

Divide the royal icing among 3 small bowls. Tint 1 bowl with orange food coloring, tint another bowl with yellow food coloring, and leave remaining bowl white. Spoon orange icing into a piping bag fitted with a small star tip (such as Wilton #16). Spoon half of yellow icing and half of white icing into separate piping bags fitted with small round tips (such as Wilton #3 or #4).

Pipe yellow and white icings on cookies in shape of daffodil petals. Keep tips of piping bags covered with a damp paper towel or plastic wrap when not using so icing doesn’t dry out.

Stir water, 1/2 teaspoon at a time, into bowls of remaining yellow and white icing until “flooding” consistency (about as thick as honey). Spoon icings into separate piping bags fitted with small round tips. Pipe icing inside petal outlines to fill them in. Let cookies stand at room temperature until icing is slightly hardened, about 30 minutes.

When icing petals have hardened, pipe small stars of orange icing in a ring in centers of cookies. Fill rings with additional white or yellow icing. Carefully fill centers of rings with orange nonpareils and/or sprinkles. Let cookies stand at room temperature until icing has completely hardened, about 2 hours. Then serve cookies, or store in an airtight container up to 3 days.