Brown the beef. Heat the olive oil in a large skillet over medium heat. Add the ground beef and cook, breaking it into crumbles as it browns. Season with the Montreal steak seasoning, brown sugar, and salt.
Add the Worcestershire. When the beef is nearly cooked through, stir in the Worcestershire sauce.
Cook the vegetables. Add the diced onion and red bell pepper and stir them into the beef. Pour in the red wine vinegar and continue cooking, stirring occasionally, until the onion and pepper have softened.
Build the sauce. Add the tomato paste and stir until thoroughly incorporated into the beef. Pour in the passata. Add 1/4 cup water to the passata container, swirl it around to release any remaining tomato, then pour it into the skillet.
Simmer until thick. Bring the mixture to a low boil, then reduce the heat and simmer until the sauce has thickened and coats the beef rather than pooling in the skillet. Taste and adjust the salt or Montreal seasoning as needed.
Toast the buns. While the beef cooks, line a large sheet pan with parchment paper and arrange the top and bottom buns cut-side up. Lightly spread the cut sides with the 5 tablespoons of softened butter.
Broil. Set the oven to HIGH broil. Broil the buns until the cut sides are golden and toasted, watching them very closely to prevent burning. Remove from the oven.
Preheat the oven. After toasting the buns, reduce the oven temperature to 375°F.
Make the garlic butter. Combine the 3 tablespoons of partially melted butter, minced garlic, and dried parsley in a small bowl. Stir until evenly combined.
Assemble the Sloppy Joes. Divide the hot beef mixture evenly among the six toasted bottom buns. Sprinkle the Colby Jack evenly over the beef, then add the toasted top buns.
Add the garlic butter. Generously brush the tops of the buns with the prepared garlic butter.
Bake. Loosely tent the sandwiches with foil and bake at 375°F for 10–15 minutes, or until the sandwiches are heated through and the cheese is completely melted. Serve hot.