Preheat the oven to 350°F and line a 9 x 13-inch baking pan with parchment paper. Allow the edges of the parchment paper to hang over the sides of the baking pan. This will help you in removing the cheesecake out of the pan by keeping the crust intact.
Prepare the graham cracker crumbs for the crust by pulsing the crackers in a food processor or placing the crackers in a ziplock bag and crushing them with a rolling pin.
In a large bowl, combine all the ingredients for the graham cracker crust and stir the mixture until it looks like wet sand. Add another tablespoon of melted butter if it still looks a little dry.
Transfer the mixture to the lined baking pan and press with your hand to form an even crust.
Take the bowl used to make graham cracker crust to combine the ingredients for the streusel topping. Mix the ingredients together and ensure the mixture comes together evenly. The mixture should form large crumbles. Set aside.
In a stand mixer fitted or with an electric hand mixer, beat sugar, cream cheese, and vanilla until smooth. Stop the mixer and scrape down the sides of the bowl. Now add the eggs, one at a time. Scrape the bowl down again and add in the pumpkin puree and pumpkin pie spice, and mix until completely combined.
Pour the pumpkin filling into the prepared pan lined with graham cracker crust. Smooth out the surface evenly using a silicone spatula. Sprinkle the streusel topping over the pumpkin filling.
Place the pan in the oven for at least 40 minutes. Check if the cheesecake is baked by inserting a toothpick in the middle. Take the pan out of the oven if the toothpick inserted comes out clean. If the toothpick comes out with the batter on it, then let it bake for 5-10 more minutes and check again.
Let your dessert cool to room temperature by placing it on a wire rack. Once cooled, place it in the fridge to chill completely.
Slice the cheesecake into square bars using a knife. You can serve the pumpkin streusel cheesecake bars with caramel sauce drizzled over the top, whipped cream, or both if desired.