Preheat oven to 400°F (200°C). Toss broccoli with 1 tablespoon olive oil, salt, and pepper. Arrange in a single layer on a baking sheet and roast for 20-30 minutes, or until lightly golden brown.

Heat the remaining 1 tablespoon olive oil in a large saucepan over medium heat. Add the onion and sauté for 5-7 minutes, or until softened.

Add the garlic and Italian seasoning to the saucepan and sauté for 1 minute more, until fragrant.

Add the chicken broth and roasted broccoli to the saucepan. Bring to a boil, then reduce heat and simmer, covered, for 20 minutes.

Carefully puree the soup using an immersion blender or transfer to a regular blender (vent the lid!).

Stir in the milk and cheddar cheese until the cheese is melted and the soup is smooth. Season with salt and pepper to taste. If desired, stir in the Dijon mustard.