Heat the oven to 350°F.  While the oven is heating, grease a 13x9x2-inch baking dish with 2 tablespoons butter.
Spread the remaining butter on the bread slices.  Cut the bread slices in half diagonally.  Arrange half the bread slices in the baking dish, overlapping as needed.  Sprinkle with half the cinnamon and half the currants.  Repeat with the remaining bread slices, cinnamon and currants.
Beat the eggs, egg yolks and granulated sugar in a large bowl with a fork or whisk.  Heat the cream and milk in a 2-quart saucepan over low heat until the mixture is warm.  Stir in the vanilla extract.
Whisk some of the warm cream mixture into the egg mixture to slowly warm up the egg mixture without cooking it (this is called tempering and it's an important step- if you add all the egg mixture straight into the warm cream mixture the eggs may cook and the mixture will curdle).  Whisk the tempered egg mixture into the remaining cream mixture in the saucepan.  Pour over the bread in the baking dish.  Let stand for 5 minutes.  Sprinkle with the brown sugar.
Bake for 40 minutes or until set.