Preheat the oven 350 degrees F. Place the beef in a bowl; season with salt and pepper. Add the flour and toss to coat. Heat the oil in a large skillet set over medium-high. Cook the beef, in batches, until nicely browned, and then set in a casserole dish. Add the onion and bell pepper to the skillet and cook 3 to 4 minutes. Add the remaining ingredients, except pesto, and bring to a simmer. Pour this mixture over the beef and stir. Cover and cook the beef in the oven 60 minutes, or until very tender. Stir in the pesto, adjust seasoning if needed, and serve.
Note: Strips of beef called “stir-fry beef” are sold in the meat department. They become mouth-wateringly tender when cooked in this ragout.