Preheat oven to 350 degrees. In a large bowl, stir together butter, sugar, salt, and egg until combined. Add vanilla, zucchini, and sour cream and stir until incorporated. Sift flour and cocoa powder into bowl and stir until combined. Stir in chocolate.
Spray two mini muffin pans with cooking spray. Fill each cup with 2 tablespoons batter and top with a walnut. Bake until a toothpick inserted in center of a muffin comes out clean, 15 to 17 minutes. Let muffins cool slightly in pans on wire racks before serving.