Make the soup: Cut the broccoli stems from the crowns. Cut the crowns into large florets and slice the stems about ½ inch thick. Set aside.
Heat 2 tablespoons of olive oil in a soup pot over medium heat for about 1 minute. Add the onion, fennel and 1 tablespoon of the salt and sauté for 10 minutes, stirring often.
Add the leek and garlic and sauté for about 10 minutes, until the onion and fennel are very soft and translucent, stirring often so the vegetables don’t brown. (If they do begin to brown, lower the heat and add a splash of water to the pan.)
Add the broccoli stems and florets and the remaining 2 tablespoons of olive oil. Stir to combine and sauté for about 10 minutes to soften. Add 1 quart of water and bring to a boil over high heat. Reduce the heat to low, cover, and cook the vegetables for about 30 minutes, until they are very tender, adding another quart of water during the cooking process. Remove from the heat and discard the thyme and bay leaf.
