Bring a large pot of water to a boil. Salt the water, add the pasta and cook until al dente.
Meanwhile, in a deep skillet or medium pot, simmer the stock and garlic over medium heat. Add the peas; cook until tender, about 3 minutes. Transfer 1 cup cooked peas to a small bowl. Transfer the remaining cooked peas, the broth and the garlic to a food processor or blender. Add the herbs, lemon juice and EVOO; season with salt and pepper. Pulse on high until a coarse puree forms, then transfer to a large bowl.
Drain the pasta, reserving 1/4 cup of the pasta cooking water. Add the cooking water and reserved peas to the sauce; toss with the pasta and season.
Divide the pasta among shallow bowls. Top with the cheese and tomatoes and season.