Preheat your oven to 400°F (200°C). Toss the broccoli florets and chopped stalks with 1 tablespoon of olive oil on a baking sheet, spreading them out in a single even layer.

Roast the broccoli in the preheated oven for 15 to 20 minutes, or until the edges are golden brown and slightly caramelized. Remove from the oven and set aside a few small, crispy florets for garnishing later.

While the broccoli is roasting, heat the remaining 1 tablespoon of olive oil in a large pot or Dutch oven over medium heat. Add the chopped onion and cook until softened and translucent, about 5 to 7 minutes.

Stir in the minced garlic and diced potato, cooking for another 2 minutes until very fragrant. Pour in the vegetable broth, scraping up any delicious browned bits from the bottom of the pot with a wooden spoon.

Bring the broth to a boil, then reduce the heat to low, cover, and simmer for 10 minutes, or until the potatoes are fork-tender. Add the roasted broccoli to the pot and simmer for an additional 5 minutes to allow the roasted flavors to meld into the broth.

Remove the pot from the heat and use an immersion blender to puree the soup until completely smooth and velvety. Alternatively, carefully transfer the hot soup in batches to a standard blender, blend until smooth, and then return to the pot.

Stir in the crumbled Stilton cheese, heavy cream, black pepper, and nutmeg over low heat until the cheese is completely melted and the soup is heated through; do not let the soup boil. Ladle into warm bowls, garnish with the reserved roasted broccoli florets and a sprinkle of extra Stilton, and serve alongside crusty warm bread.