Preheat the oven to 350 degrees F.
In a large mixing bowl with a hand mixture or in the bowl of a stand mixer with the paddle attachment, whip together the softened butter with the 2/3 cup of granulated sugar until light and fluffy. Scrape down the bowl if necessary.
Add the vanilla extract and the two egg yolks. Whip again until completely combined and fluffy.
In a separate bowl, sift the flour and the salt together. Add the orange zest and whisk gently until combined.
Add the flour mixture to the butter mixture and mix on low speed until a cohesive dough is formed.
Use a small cookie scoop to evenly divide the cookie dough into balls. Gently roll each ball in your hands until smooth.
Place the cookie dough balls on a clean plate or in a shallow bowl. Cover with plastic wrap and chill for 30 minutes.
Whisk the two egg whites together with the two teaspoons of water.
Place the finely chopped walnuts into a clean, shallow bowl.
Dip the top half of each chilled cookie dough ball into the egg white and water mixture. Then dip them into the walnuts, pressing gently so the top half of the cookies are coated in the walnuts.
Place 12 cookies on each cookie sheet lined with parchment paper or silicone baking mats.
Use your thumb to gently press an indentation into the center of each thumbprint cookie.
Bake the cookies for 14 - 16 minutes, or until just set. Be sure and rotate the pans back to front and top to bottom halfway through baking time.
Allow the cookies to cool completely on the baking sheets.
While the cookies are cooling, make the frosting.
If you are making two colors, place 1/2 cup powdered sugar into each of two bowls. Add a little food coloring to each bowl. Add one tablespoon of orange juice to each bowl. Stir the powdered sugar, orange juice and food coloring together vigorously until a smooth icing forms.
Use a small spoon to fill each cooled thumbprint cookie with a small amount of icing. Allow the icing to set up before storing or eating the cookies.