preheat the oven to 400F. Line a baking sheet with parchment paper (or just use an oven-proof skillet). Add the tomatoes and toss them in the oil and salt. Bake for 10-15 minutes, or until the tomatoes have all burst open.
In a large pot, bring about 3 quarts of water to a boil and season generously with salt (about 2 tablespoons). Cook the pasta to al dente according to the instructions. Reserve 1 ½ cups of pasta water before draining. Drain the pasta and then transfer back to the pot.
In a high-speed blender, add the ricotta, basil, walnuts, oil, lemon, salt, pepper, garlic, and ½ cup of the reserved pasta water. Blend until smooth.
Pour the ricotta sauce over the pasta along with the arugula and ½ cup more pasta water. Turn the heat to medium-low and cook for 1-2 minutes so the noodles can continue to cook and soak up that sauce. You know it’s done when the sauce coats the noodles and is no longer watery at the bottom of the pot. If the sauce looks too dry or pasty, just stir in another splash of pasta water to loosen it up. If you run out of or forget to reserve the pasta water, just use hot water instead.
Serve topped with the roasted tomatoes (if using), black pepper and a dollop of ricotta cheese, if you have some left.