Pat the chicken dry with paper towels, then season both sides with the salt, pepper, and Italian seasoning.
Lay the chicken flat in the bottom of your crockpot, keeping it in one layer.
Whisk together the chicken broth, lemon juice, and minced garlic in a measuring cup.
Pour the mixture over the chicken, then scatter the butter pats across the top.
Cover and cook on LOW for 4 hours for thighs, or about 3 hours for breasts.
Check for doneness at the early end. Chicken is safe at 165°F on a meat thermometer.
If you want a thicker sauce, stir together the cornstarch and cold water, stir the mixture into the pot, and cook on HIGH for 15 more minutes.
Finish with the lemon zest and parsley right before serving, and give everything a gentle stir.