Preheat oven to 350F/176.7C
PREPARE CHICKEN : Trim extra fat from chicken. Place seasoned flour into a bag and season chicken pieces, one at a time, by shaking in bag (shake off excess flour and discard any remaining flour mixture after all chicken is coated).
SAUTÉ CHICKEN: In a large skillet or Dutch oven, heat oil on medium heat to medium-high heat. Add chicken to the bottom of the pan and fry on one side until golden brown, about 3 minutes. Turn chicken and repeat on second side. The chicken will finish cooking later on. Drain on a paper towel over plate and set chicken aside. If your pan is not large enough to fit all the chicken pieces with some space in a single layer, fry in two batches then transfer all the chicken to a larger covered roasting pan.
SAUTE VEGETABLES: Sauté vegetables and garlic in the skillet for 5 minutes. Place chicken back in skillet (or transfer to pan with chicken if using a separate pan) and settle vegetables under and on top of chicken.
BAKE: Pour broth into bottom of skillet (or roasting pan) and sprinkle chicken and vegetables with thyme. Cover chicken, place in the oven and cook chicken for about 35-45 minutes. Vegetables should be tender and chicken should read 160F-165F/71-74C with an instant thermometer.
FINISH SAUCE AND SERVE: Remove chicken to a plate and set aside while you finish the sauce. Skim grease floating on the top and discard. Place skillet (or pan) on stove and bring vegetable and broth mixture to a boil. Pour in the cornstarch-water slurry and stir until thickened, 1 minute. Reduce heat to low, stir in spinach (if using) and cook just until wilted, about 1 minute. Taste and adjust seasonings as needed. If the sauce is too thick, add some more chicken broth or water. Place chicken back into the skillet and spoon over sauce to coat it. If serving to company, transfer the entire dish to a deep platter (or serve in the skillet), sprinkle with chopped parsley if desired and serve with mashed potatoes, rice or noodles or with crusty bread. Garnish with parsley or green onions if desired.
