Start by preparing the round steak. Trim any excess fat and pat dry with paper towels. Season flour with salt, pepper, and a pinch of paprika. Dredge the steak in the seasoned flour, ensuring it's evenly coated.
In a large skillet or Dutch oven, heat vegetable oil over medium-high heat. Once hot, carefully place the coated steak in the skillet. Sear each side until golden brown, about 3-4 minutes per side.
Remove the seared steak from the skillet and set aside. In the same skillet, add sliced onions, diced green bell peppers, and minced garlic.
Once the vegetables are tender, add a can of diced tomatoes with their juices to the skillet. Pour in beef broth (about 1 cup), Worcestershire sauce (1-2 tablespoons), a pinch of paprika.
Return the seared steak to the skillet, nestling it into the vegetable mixture. Bring the liquid to a simmer, then reduce the heat to low.
Once the steak is cooked to perfection, remove it from the skillet and place it on a serving platter. Taste the sauce and adjust seasoning if needed with salt and pepper.
Serve the Swiss steak hot, spooning the flavorful vegetable and tomato sauce over the top. This dish pairs wonderfully with mashed potatoes, rice, or even buttered noodles.