Refrigerate the mixing bowl and beaters for the whipped cream to chill while preparing the crust and custard.
For the Crust
Mix 1 1/3 cups cracker crumbs with 1/4 cup sugar and then mix in 1/3 cup melted butter until blended. Press crumbs into a 9-inch or 10-inch pie plate. Gently brush egg white on crust in a thin coating (this is optional, will give the crust more stability when sliced). Bake at 375° for 8-10 minutes until set, but not brown. Set on a wire rack to cool while making the custard and whipped cream.
For the Pumpkin Custard
In a medium saucepan, whisk 3/4 cup sugar, 1/3 cup cornstarch, and 1/8 teaspoon salt to combine. Gently whisk the 5 egg yolks into 1 cup milk then slowly add to the saucepan, stirring to combine.
Add 15 ounces pureed pumpkin and 2 teaspoons pumpkin pie spice to the saucepan and stir to combine. Cook over medium heat, continuing to stir until steam forms on the surface and soft bubbles begin to pop, about 10 minutes.
Reduce heat to medium-low and continue to cook 2-3 minutes longer, until the mixture is very thick. Remove from heat and stir in 2 teaspoons vanilla. Transfer to a mixing bowl and set a bowl in an ice-water bath; allow to cool completely (about 30 minutes), stirring occasionally. NOTE: You can skip the ice water bath if you have 2 to 3 hours to allow the custard to cool completely before mixing with the whipped cream.
For the Whipped Cream
In a small microwave-safe bowl, add 1 1/2 tablespoons water and sprinkle 1/2 teaspoon gelatin over the water; set aside for 3 minutes. Once the gelatin has softened, microwave on full power in 5-second increments until the gelatin dissolves (this can take 3-4 cycles).
Whip 1 1/2 cups heavy cream, 1 tablespoon powdered sugar, and 1/2 teaspoon vanilla in a chilled mixing bowl on medium-low speed until you see small bubbles form and the cream starts to thicken.
Increase mixer speed to medium, and once a soft trail starts to form in the cream, slowly pour in the dissolved gelatin and increase speed to high. Continue to whip until cream forms medium peaks. (See photo in Post.)
Finishing the Pie
Once the custard is cooled, gently fold 1 cup of whipped cream into the custard and then pour it into the pie crust. Cover with plastic wrap and refrigerate at least 3 hours. Cover and refrigerate extra whipped cream to serve with pie.
Use this trick anytime whipped cream is made in advance of serving: Unflavored gelatin is used to stabilize the whipped cream and the pie, but it doesn't affect the flavor or texture of the cream. This keeps it from separating when stored and firmer when sliced. If you want to keep it vegetarian-friendly, add 1 teaspoon agar-agar to the whipped cream once it reaches the soft peak stage.Total Time includes chilling time.