Preheat the oven to 425 degrees F.
In a large bowl, toss the romanesco with 2 tablespoons olive oil, 1 teaspoon salt and 1/2 teaspoon black pepper.
Spread the romanesco into a single layer on two sheet pans. Roast for 20-22 minutes until it is brown at the edges. Toss the florets halfway through roasting and rotate the sheet pans in the oven.
While the romanesco is roasting, cook the pasta until al dente according the package instructions. Reserve 1/2 cup pasta water and drain in a colander.
Heat 1 tablespoon olive oil in a large skillet or sauté pan over medium high heat.
Sauté the garlic, 1/2 teaspoon salt and 1/2 teaspoon black pepper until fragrant, about 30 seconds.
Stir the pasta into the lemon-garlic mixture.
Then stir in the roasted romanesco, lemon juice, arugula, Pecorino, walnuts and parsley. Add a splash of pasta cooking water as needed to bring everything together.