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Peel the potatoes and cut them into small pieces.
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Chop the carrots, asparagus spears, and cauliflower into small pieces.
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In a pot, over medium heat, melt the unsalted butter.
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Add the potato pieces and stir to coat them with the butter.
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Cook for 5 minutes, stirring frequently.
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Add the scallions to the pot and cook, stirring frequently until the scallions soften.
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Add the rest of the vegetables to the pot and stir to combine everything.
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Season to taste with kosher salt and freshly ground black pepper.
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Cook, stirring frequently for about 3 minutes.
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Add the broth to the pan and bring to a boil. Turn the heat down to low and simmer the vegetables until they are completely soft. About 20 minutes,
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Add the heavy cream to the pot. Stir to combine the liquids. Cook for another 5 minutes.
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Use a hand mixer to partially puree the mixture. Leave some of the vegetable pieces intact for color and texture. Alternately, transfer the mixture to a food processor or blender and pulse, until the mixture is partially pureed then return the mixture to the pot.
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Season with salt and pepper. Let cook for another 5 minutes.
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Remove from heat. Divide the soup among four soup bowls.
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Place a few of the sunflower seed pesto croutons on top of each bowl of soup, garnish with fresh parsley, if desired, and serve.