Toss the broccoli florets in the oil along with the salt and pepper, arrange them in a single layer on a large baking sheet and roast in a preheated 400F oven until lightly golden brown, about 20-30 minutes.
Heat the oil in a large sauce pan over medium heat, add the onion and saute until tender, about 5-7 minutes.
Add the garlic and thyme and saute until fragrant, about a minute.
Add the broth and broccoli, bring to a boil, reduce the heat and simmer, covered, for 20 minutes.
Mix in the milk, cheese and mustard, let the cheese melt and season with salt and pepper to taste.Puree the soup with a hand blender or in a food processor or blender and enjoy!