Trim rind from Brie. Combine Brie and next 3 ingredients in a large bowl; mix well with hands until combined. Shape cheese mixture into 1" balls. Dip balls in egg; dredge in flour. Dip again in egg; roll in breadcrumbs, pressing firmly so crumbs adhere. Place brie balls on wax paper; chill at least 1 hour.
Pour oil to a depth of 2" in a Dutch oven; heat to 350°. Fry cheese balls, in batches, until golden, about 1 minute; drain on paper towels. Serve immediately with Spicy Cranberry Dipping Sauce.