Warm oil in a medium saucepan over medium heat. Add kohlrabi and stir to coat. Add 1 to 2 tablespoons of water and cook, covered, stirring occasionally and, if necessary, add more water to cook kohlrabi until tender, about 20 minutes. Continue to cook, uncovered, until water has evaporated.
Sprinkle in flour and paprika; stir until incorporated. Add chicken stock and bring to a boil.
Stir in heavy cream and sour cream, and season with salt and pepper. Simmer until hot. Stir in finely chopped parsley before serving.
Yield: 4 servings