Combine ground beef, flour, salt, pepper, and egg in the large bowl of an electric mixer; beat at medium speed until blended, then gradually beat in milk, a tablespoon at a time, until smooth and paste-like; stir in onion.
Trim off outside leaves of cabbage. Cut off a slice about an inch thick from core end; set aside. Cut core from cabbage with a sharp knife, then hollow out cabbage to make a shell about 1 cm thick. Chop cut out pieces coarsley and cook as a vegetable for another day.
Spoon meat mixture into shell; fit cut slice back into place; tie tightly with soft kitchen string. Place stuffed cabbage, core end down, in slow cooker; add boiling water to cooker. Cook on low for 8 hours or on high for 4 hours, or until cabbage is tender; remove; keep warm.
Turn heat control to high. Combine 3 tablespoons flour and one third cup cold water in a cup; pour into liquid in slow cooker; cover; cook 15 minutes. Season to taste with salt and pepper; darken with a few drops of bottled gravy coloring.
Place stuffed cabbage on a heated serving platter; remove string. Pour gravy into a separate bowl. Cut cabbage into wedges; spoon gravy over.