Heat oil in a medium saucepan over medium-high heat. Add leek and cook until tender, about 4 minutes. Add stock; bring to a boil. Add broccoli and cook, covered, until bright green and tender, about 2 minutes.
Remove from heat. Stir in spinach, Parmesan, and tahini. Let cool slightly. Season with salt and pepper.
Working in batches, puree soup in a blender until smooth.
Top bread with avocado and radish sprouts. Season with salt and pepper, squeeze with lemon, and drizzle with oil.