Cream together the butter and brown sugar in the bowl of a stand mixer.
Add the egg yolk and vanilla, and mix until combined.
Scrape down the sides of the bowl, and add the flour and salt. The dough will be crumbly at first but will hold together as you continue to mix.
Roll the dough into 1-inch balls.
Roll each ball into the beaten egg whites, then into the chopped pecans. Place on a baking sheet. Bake for 5 minutes.
Remove from the oven and quickly press your thumb gently on top of each cookie to create an indentation. Return to the oven for 8 minutes longer.
Cool completely.
In a small bowl, stir together the powdered sugar and milk. Tint with food coloring to your desired shade.
Spoon a teaspoon or two of icing into the indentation of each cookie. Allow to harden, then serve or store for later.
Notes
Storage info: store at room temperature or in the refrigerator, for up to 2 weeks. Serve at room temperature. Freeze cookies in an airtight container for up to 3 months. I used regular liquid food coloring (McCormick) for tinting the icing. I used two drops of red and two drops of green. You can use gel food coloring if you'd like a more vibrant hue.Instead of icing, you can fill the indentation with candied fruit, Nutella, jam, hot fudge, or caramel sauce.