Preheat oven to 350 degrees F (175 degrees C).

Combine bread crumbs, 1/2 cup sugar, cinnamon, and salt in the bowl of a food processor; process for 15 seconds. Pour in melted butter; process until moist crumbs form, about 1 minute. Press into the bottom and up the sides of a 9-inch pie plate (not deep dish).

Bake in the preheated oven until deep golden brown, 25 to 30 minutes. Cool completely, about 30 minutes.

Beat pumpkin and cream cheese together in the bowl of a stand mixer until no lumps remain, about 2 minutes. Add pumpkin pie spice, vanilla extract, cinnamon, and salt; stir to combine. Transfer mixture to a bowl.

Pour cream and 1/2 cup sugar into the bowl of a stand mixer; beat on high until stiff peaks form, 3 to 5 minutes. Fold into pumpkin mixture with a rubber spatula, being careful not to deflate the cream. Pour mixture into the crust; refrigerate until set, 4 hours to overnight.