Sprinkle 1 cup of the shredded cheese evenly over the top of the sauced chicken. This first layer will melt down into the bubbling liquid as it cooks, making the sauce extra cheesy and rich.
Cover the slow cooker with the lid and cook on LOW for 4 to 5 hours, or on HIGH for 2½ to 3 hours, until the chicken is very tender and easily pulls apart with a fork. The sauce should be thick, bubbly, and deeply savory, with the chicken bites hidden underneath.
Once the chicken is cooked and the sauce is bubbling, gently stir the mixture just once or twice to fold some of the melty cheese into the sauce while still keeping plenty of chicken pieces intact.
Sprinkle the remaining 1 cup shredded cheese evenly over the top of the hot chicken and sauce. Cover again and let it sit on LOW (or switch to WARM) for about 10 to 15 minutes, just until the cheese on top is fully melted, glossy, and forms a gooey layer.
Taste the sauce and add a pinch of salt and black pepper if needed, keeping in mind that the onion soup mix is already salty.