Cream sugar and butter in an electric mixer using a paddle attachment until fluffy. Add egg white and beat for 1 minute.
Slowly add sifted flour and salt and beat at medium speed until a soft dough forms.
Cover bowl and chill in refrigerator for 30 minutes.
Preheat oven to 300ºF. Line a baking sheet with parchment paper or silicone baking mat.
Roll dough into a 1/4-inch thick rectangle on a lightly floured surface.
Cut into even rectangles, spread chocolate-hazelnut spread on half of the rectangles. Cover with a second rectangle and press down edges with a fork or fingers.
Place cookies on prepared baking sheet and bake for 15 minutes, or until golden brown.
Remove from oven and cool for 30 minutes.
Whisk powdered sugar, 3 tablespoons of milk, and vanilla extract until smooth. Add additional milk if the glaze is too thick.
Set aside 2 tablespoons of glaze in a small bowl.
Dip each cookie, chocolate-hazelnut side down, in the glaze to cover the chocolate.
Set on a wire rack to dry.
Mix remaining glaze with desired color(s) of food coloring. Drizzle colored glaze on top of the cookies.