In a large bowl, combine the beef, bread crumbs, egg, 1 tsp salt, and 1/4 tsp pepper. Mix well and form into 1 1/2 inch meatballs.
In a large skillet, heat the olive oil over medium-high heat. Working in 2 batches, add the meatballs and cook, shaking the skillet often, until lightly browned 5-7 minutes. Transfer to paper towels to drain.
Pour off all but 1 TBSP of the fat in the skillet and add carrots, onion, and celery, Cook, stirring constantly, until softened, about 3 minutes. Stir in flour and paprika and cook 1 minute. Pour in the beef broth and bring to boil over high heat, scraping up any brown bits from the bottom of the pan, season to taste with salt and pepper. Add the meatballs and caraway seeds, reduce heat to medium-low and simmer for 5 minutes.