Make the crust: Preheat the oven to 350 degrees F. Pulse the graham crackers, butter, sugar and vanilla in a food processor until fine crumbs form. Press evenly into the bottom and up the side of a 9-inch pie plate. Bake until firm, about 15 minutes; let cool completely.
Make the filling: Put the chocolate and 1/4 cup ice cream in a microwave-safe bowl and microwave in 30-second intervals, stirring, until the mixture is almost melted; whisk until smooth. Beat the remaining ice cream in a large bowl with a mixer on medium-high speed until fluffy but not melted, about 3 minutes; beat in the chocolate mixture. Freeze until firm, about 1 hour.
Meanwhile, arrange the banana slices in the pie crust. Spread the dulce de leche over the bananas and freeze until cold, about 30 minutes. Scoop the ice cream over the bananas and dulce de leche and smooth with a rubber spatula. Freeze until very firm, 4 hours.
Make the glaze: Bring the heavy cream to a simmer in a small saucepan over medium heat. Remove from the heat and whisk in the chocolate and corn syrup until melted and smooth. Let cool, whisking occasionally, until spreadable, about 15 minutes. Slowly pour the glaze over the ice cream; return to the freezer until set. Let the pie soften 10 minutes at room temperature before slicing.