Bring a pot of water to a boil. Add 1 cup peas until water starts boiling again. Add gnocchi and cook for 4 minutes. Drain.

Meanwhile, toss chicken with 1/3 cup flour in a bowl until coated. Heat 1 tablespoon oil in a skillet over medium-high heat. Transfer the chicken to the pan (reserving the flour remaining in the bowl) and add 1/4 teaspoon each salt and pepper. Cook through. Transfer the chicken to a plate.

Add the remaining 1 tablespoon oil to the pan. Add carrots, onion, 1 tsp thyme and the remaining 1/4 teaspoon pepper; cook, stirring occasionally, until the vegetables are crisp-tender. Add the reserved flour over the vegetables; stir to coat. Stir in broth and the chicken. Cook, stirring occasionally, until the stew is thickened, about 3 minutes. Add the gnocchi and peas and cook, gently stirring, until the gnocchi are hot, about 2 minutes.