In a medium saucepan or cast iron skillet, melt the butter over low heat. Stir in the olive oil and onions. Cook over medium heat until the onions begin to get tender, about 5 minutes.
Stir in the mushrooms and minced garlic. Continue cooking until the mushrooms soften slightly, about 12 minutes, stirring frequently.
Sprinkle in the flour and stir to evenly coat the mushrooms and onions.
Stir in the wine and bring the mixture back to a good simmer and continue stirring until the wine reduces down to about half, about 5 minutes or so.
Stir in the chicken broth, thyme, salt, pepper and heavy cream. Bring the mixture back to a hard simmer and cook for additional 10 minutes, stirring frequently.
Meanwhile, lightly tenderize the steaks with a meat hammer.
Sprinkle both sides of the steaks with the Mesquite Seasoning (kentrollins.com) and rub in well. Then lightly coat each side with flour.
Preheat a 12-inch cast iron skillet. Add the cooking oil. Place the steaks in the skillet over a medium heat. Cook about 2 minutes per side, to lightly brown.
Pour the mushroom soup over the top of the steaks. Top with the sliced onions. Bake at 375 for about 45 minutes or until the steaks are fork tender.