In a shallow dish, combine flour, salt, and pepper. Dredge the steak pieces in the flour mixture, shaking off any excess.
In a large skillet, heat the vegetable oil over medium-high heat. Add the steak pieces in batches, browning them on all sides. Remove the browned steak and set aside.
In the same skillet, add the chopped onion and garlic. Sauté until the onion is translucent, about 3-4 minutes.
Return the browned steak to the skillet. Add the diced tomatoes (with juice), beef broth, Worcestershire sauce, thyme, and paprika. Stir to combine.
Add the sliced carrots and celery. Bring the mixture to a boil, then reduce the heat to low. Cover and simmer for 1.5 to 2 hours, or until the steak is tender.
Serve hot over mashed potatoes or rice, if desired.