In a medium bowl, whisk together soups, cream, mustard and cheese; set aside.

Pat chicken dry and sprinkle lightly with salt and pepper. Heat oil and butter in a large, heavy skillet over medium-high heat. Brown chicken on both sides in several batches, about 3 minutes per batch. Transfer chicken to a large slow cooker.  Pour real bacon bits over chicken.

Add onion and mushrooms to skillet and cook, stirring, until tender, about 2 minutes. Stir in garlic and sauté until fragrant.  Add wine and deglaze by boiling over high heat, scraping up brown bits, until reduced by half.  Stir mushroom mixture into soup mixture and pour over chicken breasts in slow cooker.

Cook on low for 6 hours.

Carefully remove chicken breasts to serving platter or plates.  Stir tarragon into sauce and spoon sauce over chicken.

Serve with hot buttered pasta or creamy mashed potatoes.