Preheat the oven to 350 degrees.
In a large bowl cream together the butter and sugar. Add in the egg yolk and vanilla and mix until creamy and smooth.
Add in the flour and salt until a dough forms.
Pour the sprinkles into a shallow bowl.
Using a small cookie scoop, scoop the dough into 1 Tablespoon balls. Roll into the sprinkles and place on the baking sheet 2 inches apart.
Use your thumb or a teaspoon and make an indent in the center of each cookie.
Bake for 10 minutes then remove from oven and cool completely on a wire cooling rack.
To make the icing place the powdered sugar, milk, corn syrup, and vanilla in a bowl and whisk until thick and smooth.
Divide into 3 bowls. Tint one red, one white, and one blue. Carefully use a spoon to pour icing into the center of each cookie. Allow it to harden for 1-2 hours before placing in a container.