Heat oil in Dutch oven over medium heat until shimmering. Add broccoli stalks and leeks and cook until
softened, 8 to 10 minutes. Stir in garlic and cook until fragrant, about 30 seconds.
Stir in broth and water and bring to simmer. Reduce heat to medium-low, cover, and cook until broccoli stalks
are softened, about 8 minutes. Stir in broccoli florets, cover, and cook until tender, about 5 minutes.
Working in batches, process soup in blender with milk, cheddar, mustard, and ¼ teaspoon salt until cheese is
melted and soup is smooth, about 1 minute. Return soup to clean pot and bring to gentle simmer over medium-low
heat. Season with pepper to taste. Serve.