Preheat oven to 325° and line two cookie sheets with parchment paper.
In the bowl of an electric mixer fitted with the paddle attachment, cream butter and brown sugar on medium speed until light and fluffy, scraping down the bowl as needed. About 2-3 minutes.
Separate egg yolk from egg white, reserving the egg white in a bowl. Reduce speed of mixer to low and add egg yolk and vanilla. Mix on medium speed until combined, scraping down bowl as needed. About 1-2 minutes.
Reduce speed of mixer to low and add flour and kosher salt and mix until just combined. Turn mixer off and scrape down sides of the bowl with a rubber spatula, ensuring all flour has been combined. Let the dough sit while you prepare the almonds (see notes).
In a small pan, toast ¾ cup finely chopped walnuts until slightly brown and fragrant, about 3 minutes (see notes). Place walnuts in a bowl and allow to cool for a few minutes.
Roll the dough into 1 inch balls and place on a sheet of parchment paper. Slightly beat the reserved egg white and then roll dough balls in egg white, then in toasted walnuts.
Place dough balls on parchment lined cookie sheets about 1 inch apart. Bake in preheated 325° for about 5-7 minutes.
Remove cookie sheets from oven and quickly press thumb on top of cookie. Return cookie sheets to oven and bake for an additional 5-7 minutes. Cookies will still be pale in color and delicate.
Remove from cookie sheet to wire rack and allow cookies to cool completely; fill with frosting of choice. My favorite is Wilton or Betty Crocker canned cupcake icing. If you're not a fan of frosting, raspberry or apricot jam would work as well. Decorate with sprinkles or sanding sugar if desired.
Cookies can be stored in airtight containers in the refrigerator for about 15 days. To stack in cookie tins, line the bottom with parchment paper and place parchment paper between each layer of cookies.