Cut stems from broccoli and set florets aside. Peel the stems with a vegetable peeler to remove the tough outer layer. Cut the stems into slices and keep separate from the florets. You are going to add them at different times.
In a large stock pot, warm the olive oil over medium heat. Add the leeks and cook until beginning to soften, about 5 minutes. Add the potato, garlic and the sliced broccoli stems. Cook for another 5 minutes or so.
Add the broth, water, salt and a dash of pepper. Bring the mixture to a boil, then reduce the heat, partially cover and let simmer until the vegetables are tender, about 15 minutes. Add the broccoli florets and continue cooking uncovered for another 5 minutes. Off the heat, puree soup using an immersion blender. Add the half-and-half and serve with cheese, if desired.
Remove from the heat, puree soup using an immersion blender. Add the creme and serve.
A nice crusty breadstick goes very well with this.
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