Beat 2/3 cup softened butter with 1/3 cup granulated sugar until well combined. Add 2 egg yolks, 1 teaspoon vanilla extract, and 1/2 teaspoon salt, mixing until smooth. Gradually add 1 1/2 cups all-purpose flour and stir to form a dough.
Shape the dough into 24 equal-sized balls. Dip each ball into slightly beaten egg whites, then roll in the chopped walnuts until fully coated.
Place the balls on a parchment-lined baking sheet, spacing them about 1 inch apart. Using your thumb, press an indentation into each cookie ball, deep enough so the indenation remain even after baking. Bake at 350°F for about 15 minutes. Allow the cookies to cool completely on a wire rack before adding frosting.
While the cookies cool, prepare the buttercream frosting. Beat 1/4 cup softened butter with 2 cups confectioners' sugar, 1/4 teaspoon vanilla extract, and 2-4 tablespoons milk. Whip on high until smooth and fluffy. Add food coloring if desired, or leave the frosting white.
Fill a piping bag with the buttercream and pipe a generous mound into the indentations of the cooled cookies. Alternatively, use a spoon for a rustic look.