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, 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
, and parsley
. Gently fold in the cooked pasta, peas, and the cheeses, adding more reserved pasta water if necessary. Transfer to a platter and serve immediately.