Melt butter in a large skillet over medium heat. Add onions and saute until soft, about 2-3 minutes. Add garlic and flour and cook, stirring constantly for 2 minutes. While whisking, slowly pour in evaporated milk. Whisk well until smooth. Cook mixture, stirring constantly until it begins to thicken then pour into a slow cooker along with chicken broth, diced broccoli, salt, pepper and thyme. Cover with lid and cook on high heat for 2 1/2 - 3 hours or low heat for 6 hours.
Turn slow cooker off and let stand for 10 minutes and then stir in heavy cream, then add in shredded cheddar cheese and parmesan cheese and stir to blend and serve warm