Make cookie dough. Add the butter, sugar and vanilla to a bowl and beat using an electric beater on high speed for 1 to 2 minutes or until smooth and creamy. Add the flour, chopped walnuts and salt. Mix until incorporated. Shape the dough into a smooth, flat disc.
Roll and chill. Roll the dough between two sheets of parchment until it is less than ¼ inch thick. Then place the dough on a baking sheet (along with the parchment paper). Chill in the refrigerator until slightly firm, about an hour.
Cut rounds. Using a 3-inch round cookie cutter, cut out the cookies.
Cut into thirds. Place one round cut‑out cookie dough circle on a work surface. Using the same round cutter, cut two opposite sides of the circle to form a tree trunk shape.
Form trees. Take one cut edge and gently press it onto one end of the “trunk” piece, pressing lightly so they stick together. Use the other cut edge to reroll and make more cookies. Using a skewer, make about ¼-inch indentations along the bottom edge of the tree top to create a fringed branch effect. Finish cookies. Repeat with the remaining cookies, then place them on a parchment-lined baking sheet. Chill for at least 2 hours, or up to 1 day, before baking.
Bake. Preheat the oven to 350°F. Bake for 15 to 19 minutes, or until the cookies are deep golden brown. This helps give them a crisp, crumbly texture. Let them cool completely before decorating or serving.
Spread chocolate. Melt chocolate chips in a microwave until melted and smooth, about 30 to 60 seconds. Using a small spoon, spread some melted chocolate on the tree tops.
Make a fringe. Using a toothpick, make a fringe pattern on the base of the tree top.
Finish. Press one candy eyeball onto the chocolate while it’s still soft. Let the cookies sit until the chocolate sets.