Melt butter in a large skillet over medium heat. Add onions and saute until they begin to soften, about 3 - 4 minutes. Add garlic, flour and season lightly with salt and pepper then cook, stirring constantly, 2 minutes. While whisking, slowly pour in evaporated milk (whisk well to smooth).
Cook mixture, stirring constantly until it begins to thicken then pour into a slow cooker along with chicken broth, diced broccoli and thyme. Cover with lid and cook on low heat for 5 - 6 hours.
Turn heat to warm (or off) and stir in heavy cream, then add in shredded cheddar cheese and parmesan cheese and stir to blend. Season with salt and pepper to taste and serve warm.
*From about 20 oz broccoli crowns, large stems cut off and discarded (or reserved for another use), florets diced into small pieces.