Over medium heat, heat 2 tablespoons of olive oil in a medium-sized saucepan, and saute celery, onion and garlic until tender. Add a pinch of salt and pepper. Add the cut potatoes and cook for 1 minute; pour the stock into the pan. Bring to a bowl and add the broccoli. Bring the potato soup to a simmer and cook until the potatoes and broccoli are tender.
Using an immersion blender, puree the soup to preferred consistency. Add the milk and cheese. When the cheese is melted, add the seasoning to taste. Simmer on low heat for 5 minutes allowing the flavours to come together. Serve with shredded Gruyere.