Spray the inside of a slow cooker with nonstick cooking spray. Place the carrots and broccoli at the bottom of the slow cooker.
Season the chicken with salt and pepper; place the meat on top of the vegetables.
In a medium bowl, whisk together the condensed mushroom soup, condensed chicken soup, and water. Pour the sauce over the chicken.
Sprinkle the dry stuffing mix over the top of the chicken. Drizzle with melted butter.
Put a lid on the slow cooker and cook on LOW for 4-6 hours or on HIGH for 2-3 hours.
Notes
Total cooking time will vary depending on the size of your chicken and the temperature of your slow cooker. Thinner/smaller breasts will only need about 4 hours on low or 2 hours on high. Thicker cuts will need about 5-6 hours on low or 3 hours on high.
The chicken is done when it shreds easily with a fork. You're looking for an internal temp of 165°F.
Broccoli gets quite soft, so omit if you don't care for that. You can also just omit the veggies altogether, and instead cook the chicken and stuffing on their own.
If the stuffing seems too dry halfway through, add 2-3 tablespoons of broth.
Swaps: Try cream of celery for a lighter flavor or add 1/4 cup sour cream for extra tangy richness.
I prefer the flavor and texture of Pepperidge Farm brand, but Stove Top also works (use about 3 ½ cups of the dry mix).