Preheat an oven to 400 degrees. Fill a large pot with water and bring to a boil. Add the gnocchi and cook according to package instructions, but slightly undercooked. Remove gnocchi from the pot and set aside.
In a 10-inch cast-iron skillet, melt the butter over medium-high heat. Add the onions, carrots, celery, garlic, salt, and pepper. Cook the veggies until tender.
Whisk in the flour, thyme, parsely, chicken broth and heavy cream. Whisk until no lumps can be seen. Let the mixture simmer over medium-low heat for about 10 minutes or until the sauce has thickened.
Stir in the chicken and peas. Remove the skillet from the heat and top the mixture with gnocchi followed by mozzarella.
Put the skillet in the oven and cook for about 15 minutes or until the cheese is golden and brown.