Bring a large pot of salted water to a boil over high. Place a large ice bath next to the stove. Add herbs and 4 cups mixed greens to boiling water; cook, stirring constantly, until bright green and wilted, about 30 seconds. Using a slotted spoon, quickly transfer herbs and mixed greens to prepared ice bath. Let stand until cooled, about 2 minutes. Reserve water in pot. Drain greens mixture well, and press most, but not all, of liquid from mixture.

Transfer greens mixture to a blender; add nuts, Parmesan, pepper, garlic, 6 tablespoons oil, and 1 teaspoon salt. Secure lid on blender, and process until smooth, about 1 minute, adding up to remaining 2 tablespoons oil, as needed, for a looser consistency. Transfer pesto to a small bowl, and set aside until ready to use. Clean and dry blender.

Place ricotta, cream, sugar, and remaining 1/2 teaspoon salt in cleaned blender; process until smooth, about 30 seconds. Set aside until ready to use.

Return large pot of salted water to a boil over high. Add pasta, and cook according to package directions for al dente. Reserve 1 cup pasta cooking liquid. Drain pasta, and transfer to large pot; add butter, pesto, and reserved 1 cup cooking liquid. Cook over medium-high, stirring constantly, until pasta is coated in sauce. Add remaining 2 cups mixed greens; cook, stirring constantly, until wilted, about 1 minute. Divide pasta among 4 bowls, and top evenly with ricotta mixture. Stir ricotta into pasta until coated; garnish with additional nuts and Parmesan.