In a heavy bottomed stock pot or Dutch oven, melt the butter and oil over medium heat.
While the butter melts chop and clean the leeks. Using only the white and light green parts dice into 1/2 inch pieces. Place in a strainer and rinse under cold water to remove any dirt and grit that might be on the leeks.
Add the cleaned leeks to the melted butter and saute for 5 minutes or until softened. Add in the garlic and cook for another 2 minutes.
Break down the broccoli into small florets, using the stems as well. Add to the leek and garlic mixture, sprinkle with salt and pepper and stir. Cover with the 6 cups of milk and reduce to a simmer. Cover, and cook for 45 minutes or until the broccoli is tender. Stir occasionally to make sure nothing sticks or scalds on the bottom.
Using an immersion blender, blend up the soup until smooth and you no longer see any broccoli chunks. Taste for seasoning, adding more salt and pepper if needed.
Wash and peel the potatoes. Cut into 1/2 inch sized chunks and add to the pureed soup. Keep on a low simmer, cover and cook for 1 to 1 1/2 hours or until the potatoes are tender.
Taste for seasoning.
Serve with minced chives and freshly cracked pepper. If the soup looks too thick you can add 1 to 2 cups of water to thin it out. The potatoes will thicken it the longer they cook and the more they break down.
Recipe Courtesy of Megan Mitchell