Bring a large pot of salted water to a boil over high heat. Add the pasta and cook until tender but still firm to the bite (al dente), stirring occasionally, about 8 to 10 minutes. Drain the pasta, RESERVING 2 cups of the pasta water.
Meanwhile, heat the oil in a large nonstick frying pan over medium heat.
Add the shallots, garlic, carrots, salt, and pepper. Cook until tender, about 8 minutes.
Add the tomato paste and 1/2 cup of the hot pasta water. Stir to melt the tomato paste and create a sauce, adding more pasta water if necessary.
Stir in the oregano, thyme, and parsley.
Gently fold in the cooked pasta, peas, and the cheeses, adding more reserved pasta water if necessary.