Cut the onions. Peel the potatoes and carrots, then cut them into bite-size pieces. Slice the celery stalks. (Keep the onions separate from the other vegetables because they will be added to the pot before the other vegetables. Set all the vegetables aside.)
Add oil to a stock pot and heat on medium-high heat until oil is warmed.
Add the stew meat to the pot.
Sprinkle salt and paprika onto the meat, and stir to coat evenly.
Add onion pieces to the pot. Stir the meat and onions together. Cook the meat and onions for a few minutes, stirring as needed to prevent overcooking.
Sprinkle the flour over the meat and onions. Stir to coat evenly.
Add the potatoes, carrots, and celery to the meat and onions.
Add the ketchup and the beef broth to the pot, and stir to incorporate.
Heat until the liquid begins to boil. Reduce the heat to medium and allow vegetables to cook until tender, stirring occasionally, for about 10 minutes.
Using a spoon, scoop out a piece of meat, onion, potato, carrot, and celery into a small bowl with a little bit of the liquid. After cooling adequately, test each piece for tenderness. If any of the pieces are still crunchy, continue cooking and checking after a few minutes. Avoid overcooking.
Taste-test the liquid, adding more salt and pepper as needed.