Prepare two baking sheets by lining them with parchment paper or silicone baking mats. Set aside. Move the oven racks to the upper middle and lower middle positions. Heat oven to 350°F.
Place ½ cup unsalted butter, ¼ cup brown sugar, and ½ teaspoon salt in the bowl of your stand mixer fitted with a paddle attachment (or a large bowl). Cream the butter and sugar together on medium-high speed until well-mixed and slightly fluffy.
Add the egg yolk and ½ teaspoon vanilla and beat on medium-high speed again until pale and fluffy. Add 1 cup all-purpose flour and mix on low speed until a dough forms.
Whisk the egg white in a small bowl until foamy. Pour 1 ¼ cups finely chopped walnuts into a plate or shallow bowl.
Scoop the dough into 1-1½ teaspoon portions and roll each portion into a ball. Dip each dough ball first into the foamy egg whites, then roll them in the chopped walnuts until the ball is coated with walnuts.
Place the dough balls onto the prepared baking sheets, about 1½ to 2 inches apart. Use your thumb or a ½ teaspoon measuring spoon to make an indent in the center of each dough ball. Use a small spoon to to fill each indent with about ½ teaspoon of raspberry jam. Avoid overfilling.
Bake the cookies for about 10-12 minutes, or just until you see the jam start bubbling. Place the baking sheets onto wire racks and allow the cookies to cool completely on the baking sheets. Store any leftovers in airtight containers or zipper bags with sheets of parchment between layers at room temperature for up to 3 days, or in the freezer for several weeks.