Preheat your oven to 400 degrees Fahrenheit.
Toss broccoli florets with olive oil, salt, and pepper on a large baking sheet.
Roast the broccoli for 20 minutes until the edges are golden brown and tender.
Sauté the diced onion in a large pot over medium heat until translucent.
Add the minced garlic to the pot and cook for one minute until fragrant.
Stir in the flour and cook for 1-2 minutes to create a roux.
Slowly whisk in the vegetable broth and bring to a gentle simmer.
Add the roasted broccoli to the pot.
Use an immersion blender to puree the soup until the desired consistency is reached.
Stir in the heavy cream and shredded cheddar cheese until fully melted and smooth.
Season with additional salt and pepper if needed and serve warm.