To begin, combine 1 1/2 cup all-purpose flour with 1 tsp black pepper and 1/2 teaspoon of salt in a shallow dish. Stir those together.
In a large skillet, heat 2 tablespoons each of extra virgin olive oil and butter over medium high heat.
Dredge the chicken fillets in the flour mixture, shaking loose any excess flour. After you have dredged all of the chicken, do not discard the flour yet.
Brown the chicken fillets in the hot skillet. There is no need to cook these all the way through, you only need to brown both sides. Work in batches, and as you brown the fillets, place them on a plate or in a dish and set aside.
When all of the chicken fillets are browned, add the remaining 2 Tb butter to the skillet.
Add in the sliced red onion and saute over medium-low heat until the onions are golden and tender.
Sprinkle the onions with 3 tablespoons of the reserved dredging flour. Stir the flour into the onions and cook for just a minute over medium heat.
Add in the half & half, chicken broth, Cajun seasoning, thyme, and remaining salt & pepper. Stir these together and cook over medium heat until the gravy thickens and comes to a gentle boil.
Reduce the heat down to low and nestle your chicken fillets down in the gravy.
Cover and cook until the chicken is cooked through and tender, about 8 minutes.
Add the mushrooms and cook another 2 minutes.
Enjoy!
Notes
These smothered pork chops are amazing when served on a bed of mashed potatoes.