Season the round steak pieces with salt and pepper, then dredge them in flour, shaking off the excess.
In a large skillet, heat the vegetable oil over medium-high heat. Sear all the steak pieces until they're browned on both sides. Remove them from the skillet and set aside.
In the same skillet, add the sliced onion and sauté until translucent. Add the minced garlic and cook for an additional 1-2 minutes.
Add the diced tomatoes, beef broth, Worcestershire sauce, dried thyme, and bay leaf to the skillet. Mix well.
Return the seared steak pieces to the skillet, nestling them into the tomato mixture.
Cover the skillet, reduce the heat to low, and simmer the Swiss steak gently for about 1.5 to 2 hours, or until the meat is tender. You can also use an Instant Pot if you have no time to watch the steaks as they cook.
Once cooked, remove the bay leaf and discard.
Serve the Swiss steak over your preferred side dishes such as mashed potatoes, rice, or noodles, spooning the flavorful tomato and onion sauce over the top.