Heat oil in a large skillet over medium-high; add ground chuck and sirloin, and cook 5 minutes, stirring often and breaking up meat as you stir. Add onion, bell pepper, carrot, and garlic; cook, stirring often, until meat is cooked through and vegetables are very soft, 7 to 8 minutes.
Add wine, and cook, stirring often, until liquid is evaporated, 3 minutes. Stir in crushed tomatoes, brown sugar, Worcestershire sauce, salt, pepper, and crushed red pepper. Bring to a boil over medium-high, reduce to low and simmer 15 minutes, stirring occasionally. Divide mixture evenly on the bottom of buns, top with bun top, and serve immediately.
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