Cook bacon and oil in a large pot over medium heat, stirring occasionally, until bacon is golden brown and has released its grease, about 7 minutes. Add leeks, celery, onion, and butter; cook and stir until leeks have softened, about 7 minutes.
Add stock, potatoes, herbes de Provence, pepper, coriander, fennel, and salt; increase the heat to high and bring to a boil. Reduce the heat to medium-low, cover, and simmer until potatoes are just beginning to turn tender, about 8 minutes. Stir in broccoli and simmer for 5 minutes. Add milk and continue simmering until vegetables are tender, about 5 more minutes.
Purée soup with an immersion blender until smooth. Season to taste with salt and pepper. Garnish individual servings with green onions.
