Heat 2 T. olive oil in a large soup pot and add a single layer of broccoli on the bottom. Sprinkle with salt and cook on high heat for 3-4 minutes, until it is well-browned on one side only. Transfer the broccoli to a bowl or plate and repeat until you’ve seared all the broccoli. You will need to add more oil.
Sear 1 fresh whole poblano pepper on all sides (you can do this in a separate pan). Allow to cool, then remove the stem and seeds as well as any blackened skin. Chop the pepper roughly.
Lower the heat and add 2 T. butter and another 2 T. olive oil to the pot. Trim and clean 1-2 leeks, then dice finely to make 2 C. Add to the pot along with 5 minced cloves of garlic and the poblano pepper. Cook until the leeks are completely soft.
Peel and thinly slice potatoes to make 2 C. Add to the pot along with 1 quart of water, 1 tsp. salt and lots of black pepper. Bring a boil and simmer until the potatoes are tender.
Add the broccoli and simmer for another 5-7 minutes, until it is also tender.
Puree roughly in the pot with an immersion blender, leaving a few chunks for texture. Add the juice of one lemon, and season with salt and pepper.