pasta1

Position a rack in the center of the oven and heat the oven to 450 degrees F. Put a large pot with 6 quarts water and 2 Tbs. kosher salt on to boil. Grease a 9x13-inch baking dish with 1 Tbs. of the olive oil.

Heat 2 Tbs. olive oil in a 6- to 8-quart Dutch oven or heavy-based pot over medium-high heat. When the oil is shimmering, about 1 minute, add chicken and 1/4 tsp. kosher salt. Cook, stirring occasionally, until almost cooked through and nicely browned, about 5 to 10 minutes. Transfer the chicken to a bowl with a slotted spoon, add another 2 Tbs. olive oil to the pan, and brown the onions in the same manner. Return the chicken to the Dutch oven.

Using a spatula or wooden spoon, push the contents of the Dutch oven to the side. If the pan is dry, add 1 Tbs. olive oil, and then the garlic, and cook until it just starts to sizzle and becomes fragrant, about 10 seconds.

Add the chicken broth and heavy cream plus 1 tsp. kosher salt. Bring to a boil over medium-high heat, reduce to a gentle simmer, and cook for 10 minutes, stirring occasionally, so that the sauce thickens slightly.

Add the basil and rosemary and cook until they're heated through and their flavors have melded, about 5 minutes. Taste for salt and pepper.

Cook the pasta in the boiling salted water until it's just tender to the tooth, about 10 minutes. (Cook the pasta a little less than you normally might, because it will cook more in the oven later.)

Drain the pasta and add it to the sauce, along with the peas.

Add half each of the Pamigiano-Reggiano and Mozzarella to the pasta mixture and toss well. Transfer to the baking dish and spread evenly.

Top the pasta with the remaining cheese. Bake until the cheese is golden brown, about 15 minutes. Let rest for 10 minutes before serving.