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1
Remove the florets from the broccoli head and cut them into 1-inch pieces.
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2
Place half in a large bowl and half in a small bowl; set aside.
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3
Cut off the bottom of the stalk and use a vegetable peeler to trim away the woody outer layer.
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4
Cut the stalk into 1-inch pieces and place them in the large bowl with the florets; set aside.
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5
Heat the oil in a large saucepan over medium heat until shimmering.
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6
Add the onion, season with salt and pepper, and cook, stirring occasionally, until softened, about 5 minutes.
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7
Meanwhile, peel the potato and cut it into 1-inch pieces.
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8
Add the potato, chicken broth, water, and reserved pieces of stalk and florets from the large bowl to the saucepan, season with salt and pepper, and bring to a boil over high heat.
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9
Reduce the heat to low and simmer until the potato pieces and broccoli stalks can be easily pierced with a knife, about 20 minutes.
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10
Meanwhile, cut the remaining florets into 1/4-inch pieces; set aside.
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11
Using a blender, puree the soup in batches until smooth, removing the small cap from the blender lid (the pour lid) and covering the space with a kitchen towel (this allows steam to escape and prevents the blender lid from popping off).
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12
Place the blended soup in a clean saucepan and return it to low heat.
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13
Add the reserved broccoli florets and simmer until they are tender and can easily be pierced with a knife, about 10 minutes.
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14
Stir in the cheese and sour cream.
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15
Taste and season with additional salt and pepper as needed.
