Step 1

Using an electric mixer on medium speed, beat granulated sugar, powdered sugar, salt, and 1 cup butter in a large bowl until creamy, about 2 minutes. Beat in vanilla; scrape down sides of bowl. Add flour and pulse mixer a few times, then beat on low speed until flour is almost fully incorporated, about 1 minute (don’t overbeat; dough should be more clumpy than smooth). Beat in chocolate and walnuts just to blend.

Step 2

Turn dough out onto a surface and knead gently to bring together. Divide in half and form into 6"-long logs about 2" in diameter (no need to be perfect about shape of logs). Wrap in plastic and chill until firm, at least 2 hours.

Step 3

Place racks in upper and lower thirds of oven; preheat to 350°. Butter 2 standard 12-cup muffin pans. Unwrap logs and mark at ½" intervals, then cut into rounds with a chef’s knife. Place rounds in muffin cups.

Step 4

Bake cookies, rotating pans top to bottom and front to back halfway through, until golden on top, browned around the edges, and slightly soft in the center (cookies will firm up as they cool), 20–22 minutes. Let cool in pans 3 minutes, then transfer cookies to wire racks and let cool completely.Do Ahead: Dough can be formed into logs 3 days ahead; keep chilled, or freeze up to 2 months. Thaw 1 hour at room temperature or overnight in the refrigerator before slicing and baking. Cookies can be baked 7 days ahead; store airtight at room temperature.