Set the oven to 350 degrees Fahrenheit.
Heat olive oil in a skillet over medium heat, then sauté the onions until they turn translucent.
Once onions turn translucent, include mushrooms in the skillet and sauté for an additional 3-4 minutes.
Add chicken breasts that have been seasoned with salt and pepper. Cook each side for 3-4 minutes or until browned.
Make a sauce by combining chicken broth, bbq sauce, flour, and, in a measuring cup and whisking until well blended.
Once the chicken is browned, pour the sauce mixture over it and add the vegetables, thyme, sage, and rosemary to the skillet.
Gently stir to combine and bring to a simmer.
Bake the chicken in the skillet covered with a lid in the preheated oven for 20-25 minutes, or until it's fully cooked.
To complete this comforting meal, plate your smothered chicken alongside some buttery mashed potatoes and crisp-tender broccoli.
Serve hot and enjoy your smothered chicken!