Cook ground beef and sausage in a large skillet over medium heat, stirring until mixture crumbles and is no longer pink. Drain and set aside, reserving 2 tablespoons drippings in skillet.
Sauté onion in hot drippings 5 minutes or until tender. Add mushrooms; sauté 2 minutes.
Return beef mixture to skillet; stir in tomato sauce and Cajun seasoning. Simmer, stirring occasionally, 8 minutes or until liquid evaporates. Cool completely. Stir in cheese. Cover and chill thoroughly.
Roll biscuits into 4-inch circles on a lightly floured surface. Spoon 1 tablespoon beef mixture in center of each circle; brush edges with egg. Fold edges over, pressing with a fork to seal. Place on baking sheets, and cover with a damp cloth. Chill up to 2 hours, if desired.
Pour oil to a depth of 1/2 inch into a Dutch oven. Fry empanadas in hot oil, in batches, 30 seconds on each side or until golden. Drain on paper towels; serve with desired toppings.