Spread 3/4 cup chopped walnuts in a baking pan; bake in a 350° oven until golden under skins, 6 to 8 minutes. Let cool slightly. In a food processor or blender, working in batches if necessary, combine 1 pound rinsed arugula leaves (about 10 lightly packed cups), the toasted walnuts, 1/2 cup grated pecorino romano or parmesan cheese, 1/4 cup lemon juice, 1/4 cup extra-virgin olive oil, 1 1/2 teaspoons chopped garlic, and 1/4 teaspoon salt. Pulse motor a few times, just until mixture begins to come together. With motor running, slowly pour 1/4 cup more extra-virgin olive oil through feed tube or top of blender and whirl until mixture is smooth. Add more salt and fresh-ground pepper to taste.