In a large heavy saucepan, combine 1 cup of sugar and all of the milk and bring to a simmer over moderate heat.

In a small mixing bowl, dissolve the arrowroot in the bourbon. Whisk the yolks together and add them to the bourbon mixture. Measure out ½ cup of the simmering milk and whisk it into the bourbon mixture. Whisk the bourbon mixture into the saucepan of simmering milk. Stir constantly until the pudding bubbles and thickens enough to coat the back of the spoon. Remove from the heat, place a sheet of plastic wrap directly on top of the surface, and reserve.

To assemble: In a large ovenproof bowl, alternate layers of bananas and pudding, lining the sides of the bowl with the vanilla wafers as you fill the bowl. Cover the pudding with plastic wrap and refrigerate. Preheat the oven to 400°. With an electric mixer, beat the 3 egg whites until frothy. Gradually add the remaining 6 tablespoons sugar and beat until stiff and glossy. Spread the meringue over the pudding and bake for 10 minutes, or until the meringue is golden brown.