Add the chopped spinach, chicken broth, and chicken breasts to a 4‑quart slow cooker in an even layer.
Sprinkle the chopped garlic, finely chopped sweet onion, and salt and pepper over the chicken and spinach.
Cover and cook on low for 6–8 hours or on high for 4–6 hours, until the chicken is cooked through and reaches 165°F (74°C).
Just before serving, carefully remove the chicken breasts from the slow cooker and place them on a serving platter.
Stir the cream cheese, shredded Parmesan, and chopped artichoke hearts into the slow cooker until the sauce is smooth and creamy.
Spoon the creamy spinach and artichoke sauce over the chicken, top with the chopped grape tomatoes, and sprinkle extra Parmesan if desired.