Mix the sugar, arrowroot and salt in a heavy saucepan, off the heat.
Add about a 1/2 cup of milk and whisk together.
Place the pan on the stove over medium heat. Continue to stir in order to dissolve the sugar.
When you no longer feel or hear the sugar with your whisk, stir in the rest of the milk and the egg yolks.
Whisk constantly while the pudding is heating up.
As the pudding begins to thicken and bubble, switch to a spoon or spatula and reduce the heat as necessary.
The pudding is finished when it drops off the spoon in ribbons that aren't quickly absorbed into the pudding. It will take 10 to 15 minutes from the time you put the saucepan on the heat.
At this point, remove from the heat and stir in the butter and vanilla.
To assemble the puddings, put a cookie in the bottom of each ramekin and fill halfway with pudding.
Arrange banana slices on top of the pudding and place four vanilla wafers around the edge of the ramekin.
Add more pudding to fill the ramekin and top with more banana slices and cookies.
Chill for at least 2 hours before eating.