Cook the filling: Heat 1 Tablespoon olive oil in a large skillet over medium heat. Add ½ cup white onion, 1 teaspoon minced garlic, and ½ cup chopped celery. Season lightly with salt and pepper, cooking 4–5 minutes until softened.
Brown the meat: Add 1 ½ pounds ground beef and cook over medium low heat until fully browned, breaking it into crumbles. Drain any excess fat.
Make the sauce: Stir in 15 ounces tomato sauce, ¼ cup ketchup, 1 Tablespoon tomato paste, 2 Tablespoons Worcestershire sauce, 1 Tablespoon vinegar, 2 Tablespoons brown sugar, and 1 Tablespoon yellow mustard. Simmer uncovered 5–8 minutes until thickened. Taste and adjust seasoning.
Assemble the sliders: Slice the 12 Hawaiian sweet rolls or slider buns in half horizontally (keeping the top and bottom layers intact). Place the bottom half in a greased 9x13 baking dish.
Spread the sloppy joe meat mixture evenly over the rolls. Sprinkle with 1 ½ cups shredded cheddar cheese.
Place the top half of the rolls over the filling.
Top & bake: Brush 2 Tablespoons butter over the tops of the rolls. Sprinkle with 1 teaspoon sesame seeds.
Cover loosely with foil and bake at 350°F for 15 minutes. Remove foil and bake an additional 5 minutes, until the tops are golden and the cheese is melted.
Serve: Let sliders cool for 5 minutes before cutting and serving.