- 3 3/4 cups brussels sprouts, halved, cored, leaves separated
- 1/2 cup walnut halves, divided
- 2 1/2 tablespoons unsalted butter
- 1 tablespoon walnut oil plus more for drizzling
- 3 tablespoons plus 2 tsp. Champagne vinegar
- 1 1/4 teaspoons Dijon mustard
- Freshly ground black pepper
- 1/2 medium head of radicchio (about 5 oz.), cored and thinly sliced
- 3/4 teaspoon finely grated lemon zest
Blanch brussels sprouts in boiling salted water for 30 seconds; drain and immediately transfer to a large bowl of ice water to cool. Spin in a salad spinner to dry leaves (or pat dry with kitchen towels). DO AHEAD: Can be made 2 days ahead. Wrap in a kitchen towel, transfer to a resealable plastic bag, and chill.
Crush 2 1/2 Tbsp. walnuts with a rolling pin or the side of a knife; set aside. Melt butter with 1 Tbsp. oil in a small saucepan over low heat. Add shallot and crushed walnuts; cook, stirring frequently, until shallot softens, about 2 minutes. Whisk in vinegar, mustard, and sugar. Remove vinaigrette from heat; season to taste with salt and pepper. Transfer to a container, cover, and chill. Let vinaigrette come to room temperature before serving.
Place brussels sprouts and radicchio in a large bowl. Pour walnut vinaigrette over brussels sprouts mixture and toss to coat well. Transfer to a serving dish. Using a vegetable peeler, shave cheese over. Sprinkle with lemon zest and remaining walnuts. Drizzle with walnut oil.