Preheat your oven to 400°F (200°C). Line a large baking sheet with parchment paper for easy cleanup.

In a large bowl, toss the broccoli florets with olive oil, garlic powder, 1/2 tsp salt, and 1/4 tsp black pepper until evenly coated.

Spread the seasoned broccoli in a single layer on the prepared baking sheet. Roast for 20-25 minutes, or until the broccoli is tender and slightly charred at the edges. Reserve a small handful of the roasted broccoli for garnish, if desired.

While the broccoli roasts, melt the butter in a large pot or Dutch oven over medium heat.

Add the chopped yellow onion and cook, stirring occasionally, until softened and translucent, about 5-7 minutes. Add the minced garlic and cook for another minute until fragrant.

Sprinkle the all-purpose flour over the onion and garlic. Cook, stirring constantly, for 1-2 minutes to create a roux. This helps to thicken the soup and cook out the raw flour taste.

Gradually whisk in the chicken or vegetable broth, then slowly whisk in the milk. Bring the mixture to a gentle simmer, whisking frequently to prevent lumps, and cook for 5-7 minutes until slightly thickened.

Stir in the Dijon mustard, Worcestershire sauce, and ground nutmeg. Season with additional salt and pepper to taste.

Add the majority of the roasted broccoli to the soup base (reserving any garnish pieces).

If you prefer a smoother soup, use an immersion blender to partially blend the soup to your desired consistency. Leave some chunks for texture, or blend completely smooth. If you don't have an immersion blender, you can carefully transfer portions to a regular blender (vent the lid and use caution).

Reduce the heat to low. Add the freshly grated sharp cheddar cheese and the cubed cream cheese (if using). Stir constantly until all the cheese is melted and smooth. Do not boil the soup after adding the cheese, as this can cause it to separate.

Taste and adjust seasonings as needed. If the soup is too thick, add a little more broth or milk until it reaches your preferred consistency.

Ladle the hot soup into bowls. Garnish with reserved roasted broccoli florets, a sprinkle of extra shredded cheddar, chopped fresh parsley, and croutons, if desired. Serve immediately.