Preheat oven to 400.

Peel broccoli stem and chop and cut the top into florets. I cut off about 2 inches of the stem and then I chop the rest for the soup.

Cut onion into slices, about 1/4 inch thick.

Put the broccoli and the onion on a rimmed baking sheet and toss with 3 tablespoons of the oil, some salt and a few grindings of fresh pepper.

Add 5 whole cloves of garlic, unpeeled.

Roast the broccoli, onions and garlic for 30 minutes.

Meanwhile, peel and roughly chop 5 garlic cloves. Heat 1 tablespoon of oil in a large saucepan and saute the garlic for 1 minute.

When the broccoli/onion mixture is done, remove from the oven and let cool until you can handle the garlic. Snip one end off of each clove and squeeze onto the broccoli.

Pour all the vegetables into your saucepan. Add the chicken broth and the thyme. Simmer on medium-low for 20 minutes.

Puree the soup with an immersion blender or in your blender or food processor.

Add the grated cheese.

Taste the soup and add more cheese if you need to. Check the seasonings and add salt and pepper if necessary. Cheese usually has a good amount of salt so definitely taste first.