Make the dumplings: In a bowl, stir together flour and salt; add 2 tbsp. butter, and using your fingers, rub into flour until pea-size crumbles form. Add egg, and stir until dough forms; refrigerate until ready to use.
Heat remaining butter in a 6-qt. saucepan over medium-high heat; add paprika and onion, and cook, stirring, until soft, about 5 minutes.
Add vegetable stock, cauliflower, carrot and celery; season with salt and pepper, and bring to a boil.
Reduce heat to medium, and cook, stirring occasionally, until vegetables are tender, about 15 minutes.
Using a ½-tsp. measuring spoon, portion out and drop all dumpling dough into simmering soup; cook, stirring occasionally, until dumplings are cooked through, about 3 minutes.
Ladle soup and dumplings into 4 serving bowls; garnish with sour cream and parsley.