Heat 2 tablespoons of the olive oil in a large high-sided frying pan over medium heat. Add about three quarters of the onion and all of the garlic. Gently fry for about 5 minutes until soft.
Meanwhile, lightly dust the lamb with flour. Heat a little more olive oil in another pan over high heat. Add the lamb chunks in batches and cook, turning, until evenly browned. Season with salt and pepper and set aside.
Using the pan in which you've just cooked the lamb, turn up the heat, add one third of the wine, stirring and scraping the meat residue from the bottom of the pan. Allow to reduce for a minute or two.
Stir the lamb and the reduced wine into the onions. Cook over medium heat for 20 minutes.
Add the remaining wine to the lamb pan and allow the alcohol to evaporate. Then add the chicken broth and bring to a simmer.
Cover the pan and gently braise the lamb over very low heat for 1 hour 30 minutes, stirring every 30 minutes or so.
When the lamb has been cooking for about an hour, heat a little more oil in a pan over medium heat. Add the peppers and the remaining onion. Cover and cook over low heat for 15-20 minutes until soft.
Check the lamb seasoning before serving.
Place the peppers on individual serving plates and spoon the lamb on top. Finish with the cooking sauce and a touch of olive oil.