Preheat the oven to 375°F (190°C).
Season chicken pieces with salt and pepper. Heat olive oil in a large ovenproof skillet over high heat. Add chicken and cook until browned, about 2 minutes per side.
Remove chicken from skillet and set aside.
Reduce heat to medium and add onion, garlic, celery, and carrots to the skillet. Cook until vegetables are softened, about 5 minutes.
Stir in flour and cook for 1 minute.
Add chicken broth, thyme, bay leaf, and parsley. Bring to a simmer and cook for 2 minutes.
Return chicken to the skillet and spoon sauce over the top.
Bake in the oven for 30 minutes.
Remove from the oven and stir in heavy cream.
Cut croissant dough into 1-inch pieces and stir into the sauce.
Bake for an additional 15 minutes or until dough is cooked through.
Brush melted butter over the top and serve hot.
Enjoy!