Chop thyme and onion and set aside.
Add 3 tbsp butter to a large skillet set over medium heat. Add thyme, onions, and mushrooms and stir to coat. Sautee until softened, about 10 minutes, stirring occasionally.
Remove veggies and their juice to a bowl and set aside.
In a shallow dish, combine the 1/2 cup flour, paprika, 1/2 tsp onion powder, 1 tsp salt, and 1 tsp black pepper. Dredge both sides of the chicken in the flour mixture and set aside.
Add 1 tbsp butter and 1 tbsp olive oil to the skillet over medium-high heat.
Add the chicken to the skillet and cook until browned, about 5 minutes, then flip and cook another 3 minutes.
Remove the chicken to a plate and set aside; be sure to leave any drippings in the pan.
Reduce heat to low under the skillet. Whisk 4 tbsp flour into the skillet drippings to create a roux over. (If your pan is too dry, you can add another tbsp. of butter). Cook for one minute, whisking constantly, until you have a thick, blonde or dark blond paste/roux.
Increase the heat to medium-high. Slowly whisk the chicken broth into the roux until you have a sauce. Let simmer, whisking occasionally, until the sauce has thickened to gravy consistency, 5-10 minutes.
Once gravy is thickened, add the veggies and their juices back into the pan. Stir to combine. Taste and add more salt/pepper if you like.
Add the chicken pieces back to the pan, nestling them into the gravy.
Cover the skillet and reduce the heat to low, maintaining a vigorous simmer, and cook 10 minutes or until the chicken is cooked through. Sprinkle with chopped thyme or parsley if desired, then serve immediately with broiled broccoli (see below) and a carb to soak up all that delicious gravy!
While the chicken cooks, make your broccolini.