Preheat oven to 350°F. Grease 3-qt. shallow baking dish with some of the butter.
Spread remaining butter on bread slices. Cut each slice in half diagonally. Layer half the bread slices in prepared dish. Sprinkle with half the cinnamon and half the currants. Repeat with remaining bread slices, cinnamon and currants.
Mix eggs, egg yolks and granulated sugar.
Heat cream and milk in medium saucepan over low heat until warm. Stir in vanilla. Stir some of the cream mixture into the egg mixture. Return egg mixture to remaining cream mixture. Pour over bread. Let stand 5 min. Sprinkle with brown sugar.
Bake for 35 to 40 min. or until custard is set. Serve warm or at room temperature.
Tip: Substitute 8-cup glass measure for saucepan. Place cream and milk in 8-cup glass measure. Microwave on medium about 7 min. or until warm.
Make ahead: Prepare recipe and assemble in prepared dish. Cover and refrigerate overnight. Bake at 350°F. for 40 min. or until custard is set.