Place the chicken thighs in the slow cooker. Add the minced garlic, chicken broth, heavy cream, 1/2 cup of the Parmesan cheese, thyme, salt, and pepper. Stir gently to combine.
Cover and cook on low for 6 hours or on high for 3 hours until the chicken is tender.
About 30 minutes before the chicken is done, bring the water to a boil in a medium saucepan. Slowly whisk in the cornmeal and reduce the heat to low.
Cook the polenta for 20 to 25 minutes, stirring often, until it thickens. Stir in the butter and the remaining 1/2 cup of Parmesan cheese. Season with a pinch of salt if needed.
Spoon the polenta into bowls and top with the chicken thighs and some of the garlic cream sauce from the slow cooker.