Place the chicken pieces into the slow cooker, spreading them out evenly.
Pour in the chicken broth, then sprinkle with dried thyme, salt, and pepper to season the chicken.
Mince the garlic cloves and add them to the slow cooker, releasing a fragrant aroma as the garlic begins to cook.
Cover the slow cooker and cook on low for about 4 hours, until the chicken is tender and cooked through, and the house smells garlicky and herbaceous.
About 15 minutes before serving, add the cream cheese chunks to the slow cooker, then gently stir until melted and incorporated into the sauce, creating a luscious, velvety texture.
Pour in the heavy cream or coconut milk, stirring to combine for extra richness, and let it simmer uncovered for a few minutes until slightly thickened and fragrant.
Taste the sauce and adjust seasoning with additional salt or pepper if needed. Sprinkle chopped parsley over the top for a fresh, vibrant finish.
Serve hot over rice, noodles, or mashed potatoes, spooning the velvety sauce generously over the tender chicken.