Preheat the oven to 300 degrees . Butter a 9-inch square baking dish. In a medium saucepan, bring 3 cups milk to a simmer. Add the rice and sugar and stir until the sugar is dissolved. Spread the mixture in the prepared dish, cover loosely with foil and bake for 30 minutes. Stir and continue baking until the rice is tender, about 30 minutes more. Remove from the oven and stir in the remaining 1 cup milk and the currants; let cool.
Divide the pudding among 6 whiskey glasses and top with Irish cream. Serve with the cookies.