In a large pot, preferably a Dutch oven, heat the oil over medium heat until shimmering. Add the butter and stir until melted.
2 tbsp olive oil, 2 tbsp unsalted butter
Add the leek, carrot, celery, and garlic. Cook, stirring frequently, until they are tender, about 8 minutes.
1 leek, 1 carrot, 1 celery rib, 1 garlic clove
Stir in the broccoli.
1½ heads broccoli
Sprinkle the broccoli mixture with the flour and mix well.
¼ cup all-purpose flour
Stir in the broth and bring to a simmer over medium-high heat.
5 cups chicken broth
Reduce the heat to medium and simmer, with the lid on, but ajar, until the broccoli is very tender, about 20 minutes. Remove form the heat.
Purée the soup with a hand-held immersion blender, or very carefully, working in batches, transfer the soup to a blender and purée.
Add the soup back into the pot and simmer over medium-low heat.
A handful at a time, add the Cheddar cheese to the soup, and let it melt.
8 oz cheddar cheese
Season with salt and pepper.
2 tsp Kosher salt, 1 tsp black pepper
Serve piping hot topped with a few blanched florets!