Heat olive oil in a large pot or Dutch oven over medium-high heat. Add chicken pieces and cook until browned on all sides, about 5-7 minutes. Remove chicken and set aside.
In the same pot, add onion, carrots, and celery. Cook until softened, about 5 minutes. Add garlic and cook for 1 minute more.
Sprinkle flour over the vegetables and stir to coat. Cook for 1-2 minutes, stirring constantly.
Gradually pour in chicken broth while stirring to prevent lumps. Add thyme, rosemary, and bay leaf. Bring to a boil.
Return the chicken to the pot. Reduce heat to low, cover, and simmer for 30 minutes, until chicken is tender and vegetables are cooked through.
Stir in frozen peas and cook for 2-3 minutes. If using, stir in heavy cream for a richer stew. Season with salt and pepper to taste. Remove bay leaf. Garnish with parsley before serving.
Tips
To thicken the stew further, mash some of the vegetables against the side of the pot.
Store leftovers in an airtight container in the refrigerator for up to 3 days.