Like the chocolate-and-vanilla retro classic, this gingery icebox cake requires some make-ahead assembly--but no baking. And it's absolutely drool-worthy.
In a large mixing bowl, beat cream, 1/2 cup powdered sugar, the vanilla and nutmeg with an electric mixer on medium speed until stiff peaks form. Fold in pumpkin and remaining 1/2 cup powdered sugar. Transfer mixture to a disposable piping bag or resealable plastic bag. Cut off the tip or corner of bag to pipe.
Spread a thin layer (about 1/2 teaspoon) of dulce de leche on each gingersnap cookie, then pipe about 2 teaspoons cream mixture on top. Stack cookies together to make 4 stacks of 10 cookies. Lay the first cookie stack on its side at the end of an oval or rectangular platter (pipe a bit of cream under it to hold it in place). Lay the other stacks next to the first one, so they touch (imagine tin cans lying next to each other on their sides). Freeze 20 minutes.
Pipe the outsides of the stacks all over with remaining cream mixture, then spread evenly using a knife dipped in water to smooth and square edges. Loosely cover in plastic wrap (insert a few toothpicks in top to keep plastic from sticking to cake). Refrigerate at least 1 hour or up to overnight.
To serve: Warm remaining dulce de leche in microwave, thinning with a little milk or cream if needed. Slice cake crosswise into eight slices (through the center of each cookie stack), cleaning the knife between each cut. Garnish each slice with a drizzle of dulce de leche and a sprinkle of cinnamon.
Or use Nabisco gingersnaps and reduce to 32 cookies, using 8 cookies per stack.