In a large mixing bowl, combine the sweetened condensed milk, pumpkin purée, pumpkin spice, vanilla extract and salt. Whisk until well combined. Set aside.
In a stand mixer fitted with the whisk attachment, beat the heavy cream on medium-high speed until stiff peaks form, about 3 minutes.
Using a rubber spatula, gently fold the whipped cream into the sweetened condensed milk mixture until well combined.
Layer about ¼ of the pumpkin cream in an 8x4-inch bread pan. Drizzle about ¼ of the caramel sauce and sprinkle ¼ of the crushed gingersnaps on top. Repeat these layers 3 more times until the ice cream and mix-ins are used up. Swirl the top of the ice cream with a toothpick.
Cover the pan with plastic wrap and freeze until firm, 8 hours. Ice cream can be stored in the freezer, covered, for up to 3 weeks.
To serve, let the ice cream warm on the counter for 5 minutes before scooping. Drizzle with more caramel and crushed gingersnaps. Enjoy!