In a large stockpot, heat oil and sauté the onion for 5 to 7 minutes over low to medium heat. Add potatoes, broccoli, and stock; bring to a boil. Reduce to a simmer and cook, covered, for 12 to 15 minutes or until broccoli and potatoes are tender when pierced with a fork.
Remove the mixture from stove top; allow to cool a bit. Pour the mixture and cheese into a blender; puree. (Or use a handheld blender to do it right in the stockpot.)