In a bowl, mix together pureed sweet potatoes, milk, eggs and 1/3 cup granulated sugar until smooth.
Preheat the oven to 350 degrees F. Fill the tray on the baking sheet in the oven with 1.5 cups hot water.
In a bowl, mix together crushed graham crackers, 1 tablespoon granulated sugar and melted butter. Transfer to a 9 inch pie pan and press the mixture on the bottom and up the sides of the pan. Put the filling into the crust and bake for 30 minutes.
Take the pie pan out of the oven and pour the honey on top. Let cool on a wire rack for 20-30 minutes. Then refrigerate for 2-3 hours.