Spray Crockpot insert with cooking spray, or line with slow cooker liner. Scatter onion slices and sliced mushrooms in bottom of Crockpot insert.
Liberally season both sides of chicken breasts with plenty of salt and lots of freshly cracked black pepper. Place in Crockpot on top of onions and mushrooms.
In medium mixing bowl, whisk together cream of mushroom soup, Italian dressing mix, cream cheese, dry white wine, and melted butter until completely smooth, then pour mixture over chicken breasts.
Cook chicken mixture, 5 to 6 hours on low or 3 hours on high if uncovered. If cooking covered, sauce will be thinner and chicken will cook faster, likely only 3 to 4 hours on low.
Once chicken reaches internal temperature of 160° Fahrenheit, transfer chicken breasts to cutting board or plate. If desired, add ¼ cup water from cooking pasta or ¼ cup chicken broth to thin sauce, stirring well to incorporate before adding more liquid.
Once desired sauce consistency is achieved, plate chicken on top of pasta, rice, mashed potatoes, or mashed cauliflower. Cover with additional sauce, garnish with fresh parsley or chives, and serve immediately.