Cut the leek in half lengthwise, finely chop it and add it to a dutch oven or a pot with the butter. Fry gently on low heat for 5 minutes until the leek is soft.
In the meantime, peel the potato and cut it into ½ inch (1.3 cm) cubes. Next, chop the broccoli into equally sized pieces, including the stem and leaves.Add chopped broccoli, diced potatoes, fresh thyme leaves, salt, and black pepper to the pot.
Cook on medium heat for two minutes. Stir often.
Add the vegetable broth and simmer for 20 to 30 minutes, or until the potatoes and the broccoli are fork tender. Stir occasionally.
Blend the veggies with an immersion blender until smooth; don't over-blend. We think some broccoli texture is desirable in this soup.Add more vegetable broth if you like a thinner soup.
Taste, adjust for salt, and serve in a bowl. You can sprinkle with red pepper flakes, croutons, roasted chickpeas, and a drizzle of extra virgin olive oil.