In a large bowl, combine the flour, salt, and black pepper. Dredge the pieces of round steak in the flour mixture, shaking off any excess.
In a large skillet, heat the vegetable oil over medium-high heat. Add the floured steak pieces and brown them on all sides, about 5-7 minutes. Transfer the browned steak to the slow cooker.
In the same skillet, add the sliced onion, bell pepper, and garlic. Sauté for about 3-4 minutes until the vegetables are softened. Add them to the slow cooker.
Pour the diced tomatoes (with juice), beef broth, Worcestershire sauce, thyme, and paprika over the steak and vegetables in the slow cooker. Stir to combine.
Add the sliced carrots and green beans on top. Cover and cook on low for 6-8 hours or on high for 3-4 hours, until the steak is tender and the vegetables are cooked through.
Once cooked, taste and adjust seasoning if necessary. Serve hot over mashed potatoes or rice.