Preheat oven to 325 degrees F.

Place flour on a large plate and set aside. Cut round steak into serving pieces. Salt & pepper as desired. Dredge steak in flour (really press in well), then use the edge of a sturdy plate to pound the meat. Repeat this pounding process on both sides until the meat is about 1/2 inch thick and noticeably more tender. Add a bit more flour if it becomes sticky. A meat mallet may be used instead, the large pointed side.

Heat vegetable oil in a large ovenproof skillet (or Dutch oven) over medium heat; cook the onions & floured beef in the hot oil until the meat is golden brown, turning once. This will likely have to be done in batches, but the onions are best done in the first batch, then left in the pan to slowly brown and color through as the second batch cooks.

Return all meat to pan, strew with onions. Strew the bell pepper slices across the top. If you need to layer the meat, make sure each layer contains onion & pepper. Mix tomatoes with salt and pepper, pour over the top. Check the bottom of the pan. Liquid should come up nearly to the top but not over the first layer of meat. Add a little water if needed.

Bring to a simmer, cover tightly and place in a 325-degree oven until done, when meat is tender and no longer chewy, but still holding together, about 1  1/4 to 1 1/2 hours. Remove meat, stir sauce and vegetables together and serve with meat.