Heat the oven to 425°F and oil a rimmed sheet. Soak breadcrumbs in milk for 3 minutes, then mix gently with beef, egg, salt and pepper. Divide into 24 equal portions.
Flatten each portion, place a cheddar cube in the center and wrap the meat around it, sealing all seams. Roll gently into a ball and bake for 16 to 20 minutes until the meat reaches 160°F when checked beside the cheese pocket.
Meanwhile, whisk mustard, ketchup, vinegar, brown sugar, broth, Worcestershire and paprika in a saucepan and bring to a simmer. Transfer hot sauce to a 4-quart slow cooker and add hot meatballs.
Cover and cook on HIGH for 2 hours, turning carefully through the sauce after 1 hour, until the meat reaches 165°F and the glaze coats the outside. Uncover for the last 10 minutes if the sauce needs reducing.
Switch to WARM only while serving and verify the food stays at least 140°F. Serve about 3 meatballs per appetizer portion.