In a large bowl, stir together sweetened condensed milk, vanilla, espresso, pumpkin pie spice, and pumpkin puree.
In a separate large bowl, beat heavy cream with an electric hand mixer until it reaches stiff peaks.
Fold whipped cream into the sweetened condensed milk mixture gently until fully incorporated.
Pour mixture into a standard loaf pan. Freeze for 6 hours.
When the ice cream is set, pulse gingersnap cookies, sugar, and melted butter until it forms a crumble.
Add the crumble to the top of the ice cream. Serve immediately.