Shaved Brussels Sprouts With Brown Butter Vinaigrette, Walnuts & Pecorino

Ingredients

• 1 pound Brussels sprouts
• 1 pinch kosher salt
• 6 tablespoons chopped, toasted walnuts, divided, plus more for topping
• 2 tablespoons unsalted butter
• 1/2 small shallot
• 1 1/2 teaspoons Dijon mustard
• 1 tablespoon sherry vinegar or apple cider vinegar
• 1 1/2 teaspoons water
• 1/4 cup grated pecorino, plus more for topping
• several grinds black pepper