Brown the beef and pancetta in the oil in a large skillet until golden brown, about 5 minutes. Stir in the garlic, carrots, celery, onions and bell peppers and sprinkle with salt and black pepper. Add the tomatoes, cheese, ketchup, paprika, sugar, vinegar, Worcestershire, cayenne, thyme and jalapeno and bring to a boil. Reduce the heat to a simmer and cook, covered, 15 minutes. Taste and adjust the seasoning, and then stir in chives.
Toast the buns in a grill pan. Divide the beef between the buns on 4 plates and garnish with shaved cheese.