Cut squash into 1/2 chunks, In a roll pan put squash , shallots, 1 tablespoon oil, 1/8 teaspoon salt, and 1/8 teaspoon freshly ground black pepper to evenly coat. roast for 25 minutes until tender. Using a slicer cut brussels sprouts crosswise into very thin slices. In a large bowl toss sprouts, walnuts, lemon juice, 1/4 teaspoon salt, 1/4 teaspoon freshly ground black pepper, and remaining 2 tablespoons oil until well mixed. Spread on serving platter. Top with squash mixture and Pecorino shavings.