Heat olive oil in a large pot over medium heat. Add onion and garlic, sauté until softened.
Add diced potato and chopped broccoli. Stir to coat with oil.
Pour in the vegetable broth, bring to a boil, then reduce heat and simmer for 15 minutes until vegetables are tender.
Use an immersion blender to puree the soup until smooth (or transfer to a blender in batches).
Stir in the milk (or cream) and Stilton cheese. Cook for 2–3 more minutes until the cheese melts.
Season with salt and pepper to taste. Serve warm with crusty bread.