In large skillet melt butter over medium heat.
Saute onions until they become transparent, about 3-4 minutes.
Add garlic and flour, as well as a little salt and pepper to flavor.
Cook for 2 minutes, stirring constantly.
Using a whisk, slowly add in evaporated milk and stir well to make it smooth.
Cook mixture until it begins to thicken, then pour into slow cooker with chicken broth, broccoli & thyme.
Cover and cook 2 1/2 - 3 hours on high or 6 hours on low.
Turn heat off (or warm if you have that option), and add in heavy cream, shredded cheddar cheese and parmesan cheese.
Season with salt and pepper and enjoy!