In a large bowl, combine the graham cracker crumbs, butter, sugar and salt until evenly moistened. Reserve 1/4 cup of the crumb mixture for garnish and set aside.
Press remaining crumb mixture into bottom of an 8 or 9 inch springform pan. Place in refrigerator while preparing the filling.
In a separate bowl with an electric mixer, beat the cream cheese, pumpkin, sugar, pumpkin pie spice and vanilla until smooth.
Fold in 1 cup of whipped topping with a spatula.
Scrape cheesecake mixture into the crust and spread top evenly. Garnish remaining whipped topping and graham cracker crumbs. Cover with plastic wrap and refrigerate for 3 hours before serving.
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Notes
Remove the cream cheese from the refrigerator about 30 minutes before mixing. I usually cut mine up into cubes so that it will soften faster. If you mix the cream cheese when it's still cold, you could end up with little solid bits in your cake.
Be sure to chill this cheesecake in the refrigerator for at least 2-3 hours, even longer is better. If you don't let it chill, it will not firm up.