To make the sloppy joe sauce, combine the vinegar, ketchup, tomatoes, brown sugar, and Worcestershire sauce in a bowl and mix well.

To make the sloppy joe filling, brown the ground beef in a skillet over medium heat, stirring constantly, and season with salt and pepper. When the meat has browned, drain it and return it to the skillet.

Add the celery, onion, and garlic to the skillet, and stir to combine. Cook until the celery and onion are just beginning to soften.

Add the sloppy joe sauce to the skillet and simmer for 15 minutes.

Toast the slider buns under the broiler until they just begin to brown.

To serve, spoon the sloppy joe filling over the bottom buns and cover with the top buns.