Heat the olive oil in a large pot over medium heat. Add the onion, celery, and leek, cooking until softened but not colored, about 5-7 minutes.
Add the diced potato and broth to the pot. Bring to a boil, then reduce the heat and simmer until the potato is tender, about 10-15 minutes.
Add the broccoli florets to the pot and cook until they are just tender, which should take about 5 minutes. You want to preserve their green color and nutrients.
Remove from heat. Add the crumbled Stilton cheese to the soup, stirring until the cheese is melted and the soup is smooth.
Blend the soup using an immersion blender or in batches using a regular blender until smooth. Season with salt and pepper to taste.
Serve hot, with a swirl of cream if desired, for an extra touch of richness.