Prep the pan. Position a rack in the center of the oven and heat to 350°F (175°C). Lightly grease a 9x13-inch pan, then line it with a sheet of parchment that overhangs the two long sides. This sling will let you lift the whole slab out later.
Make the crust. Melt the butter in a microwave-safe bowl in 20-second bursts, just until liquid. In a large bowl, stir the gingersnap crumbs and 2 tablespoons brown sugar together, then pour in the butter. Mix until the crumbs look like damp sand and hold together when pinched.
Press and bake the crust. Tip the crumbs into the pan and press them into an even, firm layer across the bottom, using a flat-bottomed cup to pack the corners and edges tightly. Bake for 10 minutes, until fragrant and slightly darker at the edges. Set the pan on a wire rack. Leave the oven on.
Mix the filling. In a large bowl, whisk the eggs until the yolks and whites are blended. Whisk in the granulated sugar, 1/2 cup brown sugar, cinnamon, ginger, nutmeg, cloves, salt and 2 teaspoons vanilla. Add the pumpkin and whisk until smooth, then whisk in the evaporated milk until no streaks remain.
Fill the pan. Pour the filling over the warm crust and spread it to the corners with a spatula. Tap the pan gently on the counter to release large air bubbles. If you are using a rimmed baking sheet, set the pan on it now.
Bake. Bake for 45 to 55 minutes, checking at 45 minutes. The bars are done when the edges are set and the center still jiggles slightly in a spot about 2 inches wide. A knife inserted about an inch from the center should come out clean, and the center should read about 170–175°F (77–79°C) on an instant-read thermometer if you want to check. If the top or edges brown before the center sets, loosely tent the pan with foil.
Cool. Cool the pan on a wire rack for about 1 hour, until it is no longer warm to the touch. The center will firm up as it cools.
Chill. Cover loosely and refrigerate for at least 3 hours, or overnight, until completely cold and firm. Cold bars are what cut cleanly.
Cut. Use the parchment overhang to lift the slab onto a cutting board. Cut into 4 rows by 6 columns to make 24 bars, each about 2 1/4 by 2 inches. Press straight down with a long, sharp knife and wipe the blade clean between cuts. A gentle sawing motion helps through the crust.
Top and serve (optional). Whip the cream with the powdered sugar and 1/2 teaspoon vanilla until medium-stiff peaks form. Add a small dollop to each bar just before serving and dust lightly with cinnamon.