Heat the oven to 350°F before preparing the beef. A fully heated oven keeps the braise steady from the moment the covered Dutch oven goes in.
Pound the round steak with a meat mallet until it is ½-inch thick throughout. The steak should look evenly flattened, with no thick, untouched sections around the edges.
Mix the flour, paprika, garlic powder, black pepper, and salt to taste, then coat the steak thoroughly in the seasoned flour. A light, even coating should cover the surface without forming thick clumps.
Warm 1 tablespoon of olive oil in a Dutch oven over medium heat, then brown the floured steak on both sides, adding more olive oil as needed. Listen for a lively sizzle and look for a deep golden-brown crust before moving each piece.
Arrange the chopped onions and carrots across the bottom of the Dutch oven, then set the browned steak over them. The vegetables form a flavorful bed that softens into the gravy as the beef cooks.
Pour in the diced tomatoes with their juices, beef broth, and Worcestershire sauce, leaving out the cornstarch, then cover the pot and braise for 2 ½ to 3 hours. The gravy should bubble gently around the edges, and a fork should slide into the beef with little resistance when it is ready.
Spoon the steak and tomato gravy over mashed potatoes for serving. The finished sauce should look glossy and lightly thickened, with tender vegetables tucked around the beef.