Make the crust:.
Preheat the oven to 375°F.
In a food processor, process the graham crackers, granulated sugar and cinnamon until finely ground. Add the butter, oil and milk, and process until thoroughly moistened.
Press the crumb mixture into a 9-inch pie plate. Bake for 10 to 12 minutes. Cool on wire rack.
Meanwhile, make the filling: In a medium saucepan, combine the brown sugar and cornstarch. Whisk in the milk until well combined. Bring to a simmer over medium heat. Simmer while whisking until thickened, about 1 minute.
Gradually beat 1/2 cup of the hot pudding into the beaten egg, then whisk the egg mixture back into the pan. Cook until the pudding starts to simmer. Remove from the heat and stir in the vanilla. Set aside to cool lukewarm.
Thinly slice 2 of the bananas and fold into the cooled pudding. Spoon the filling into the pie shell, smoothing the top. Slice the remaining banana and arrange decoratively on top of the pie.
In a small saucepan, melt the fruit spread over medium heat. Brush the melted jam over the banana slices. Chill the pie for several hours to firm it up and make easier to slice.