First, prepare the vegetables. Remove the greens from the kohlrabi and set aside. Cut the kohlrabi into quarters and remove the peeling with a paring knife. Once peeled, cut the kohlrabi into medium dice, and set aside. Wash the leaves and separate the leaf portion from the thick rib and stem. Rough chop the leaves and set aside.
Roughly chop the garlic scapes and set aside. Remove the green tops from the scallions and slice the lower onion portion. Set aside with the garlic scapes. Finely slice the green tops and set aside to use as a garnish for serving the soup.
Warm the oil or butter in a medium saucepan over medium heat. Add the onions and garlic scapes and sauté until fragrant and tender. Sprinkle the flour and 1 ½ tsp paprika over the onion & garlic mixture and stir to combine all of the flour. It should make a light paste. Add 1 cup of the chicken or vegetable stock to the pan and stir to incorporate the flour paste into the liquid. Once well combined with no lumps, add the remaining stock along with the diced kohlrabi, kohlrabi leaves and 2 tsp salt and freshly ground black pepper.
Bring the soup to a gentle simmer over medium-to-medium high heat. Simmer, uncovered, until the kohlrabi is just tender when tested with a fork, about 20 minutes.
Remove from the heat and carefully puree the soup either with an immersion blender in the pan you prepared the soup in, or carefully transfer the soup to a blender. Purée until smooth, then return the soup to the original pan. Heat the soup over low heat and carefully stir in the heavy cream and sour cream, being careful that the mixture does not come to a boil.
Once warmed through, taste the soup. Add additional salt, pepper, and/or paprika to your liking. Stir in the chopped fresh parsley and serve with the green onion tops.
