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