1. Heat olive oil in a heavy skillet over mediumheat. Add onions, cook until lightly brown, about 5 minutes.
2. Add garlic and diced peppers, cook until peppersare soft.
3. Add stock, stir. Add turkey. Cook and stir,breaking up the meat, until it begins to brown, about 2 minutes.
4. Add tomato sauce, brown sugar, paprika, salt,and black pepper. Cook and stir until liquid is reduced, about 5 minutes.
5. Stir in Worcestershire sauce and cocoa powder. Cook, stirring frequently, until meat is cooked through and liquid is reduced and thick, 20 to 30 minutes, adding up to 1 cup water if needed.
6. Preheat the oven's broiler. Set the oven rack about 6 inches from the heat source. Toast hamburger buns under the preheated broiler until golden, 2 to 3 minutes.
7. Remove turkey mixture from the heat; mix in cheese and green onions.
8. Serve on toasted hamburger buns.