Bring a large pot of salted water to a boil. Add about 1/4 cup olive oil to the water to help prevent pasta from sticking. Add the ravioli and cook until al dente, stirring occasionally, about 5 minutes. Drain the ravioli, reserving 1/2 cup of the cooking water. Toss the ravioli with the remaining oil to coat.
Meanwhile, bring the marinara sauce to a simmer in a medium saucepan over medium heat, whisking often. Whisk in the ricotta and enough reserved cooking water to thin the sauce to desired consistency. For a thicker sauce, use less pasta water; for a thinner sauce, add more water. Return the sauce to a simmer. Season the sauce to taste with salt and pepper.
Spoon 3 tablespoons of sauce over the bottom of each of 6 bowls. Arrange the ravioli over the sauce. Drizzle the remaining sauce over the ravioli. Sprinkle with the Parmesan and the basil, and serve.