Place chicken in the slow cooker crock. Top with 2 tablespoons melted butter; sprinkle with Italian dressing mix.
Cover, and cook on High for 3 hours.
Heat the remaining 2 tablespoons of butter in a large skillet over medium heat. Stir in onion and garlic; cook and stir until onion is soft, about 5 minutes. Mix in the cream of chicken soup, chicken broth, and cream cheese. Pour mixture over the cooked chicken in the slow cooker.
Cover, and continue to cook on Low until chicken in fork tender and the sauce has thickened, about 1 additional hour.