Preheat your oven to 325°F (165°C). Line a 9x13-inch baking pan with parchment paper, leaving some overhang on the long sides as handles. Lightly grease the parchment and any exposed sides of the pan with butter or nonstick spray.

Crush the gingerbread cookies or gingersnaps into fine crumbs using a food processor or a zip-top bag and rolling pin. In a medium bowl, combine the cookie crumbs, 2 tablespoons granulated sugar, 1/2 teaspoon ground cinnamon (if using), and 1/4 teaspoon fine sea salt. Pour in the melted butter and stir until the mixture looks like wet sand and holds together when squeezed.

Transfer the crumb mixture to the prepared pan and press it firmly and evenly into the bottom, using the bottom of a measuring cup or glass to compact it well and reach into the corners. Bake the crust for 8–10 minutes, just until fragrant and set. Remove from the oven and let cool slightly while you make the filling.

Reduce the oven temperature to 300°F (150°C) to prepare for baking the cheesecake layer.

In a large mixing bowl or stand mixer fitted with the paddle attachment, beat the softened cream cheese on medium speed until very smooth and creamy, about 2–3 minutes. Scrape down the bowl and beater several times to prevent lumps.

Add the granulated sugar and brown sugar to the cream cheese and beat until fluffy, about 1–2 minutes. Beat in the molasses and vanilla extract until fully combined.

Add the Greek yogurt or sour cream and mix on low speed until smooth. Sprinkle in the cinnamon, ginger, nutmeg, cloves, and salt, then mix on low just until the spices are evenly distributed.

Add the eggs one at a time, mixing on low speed after each addition just until incorporated. Avoid overmixing at this stage to prevent incorporating too much air, which can cause cracks. Give the bowl a final scrape and gently stir by hand to catch any hidden lumps.

Pour the spiced cheesecake filling over the slightly cooled crust and smooth the top with an offset spatula or the back of a spoon. Tap the pan gently on the counter a few times to release any large air bubbles. Bake at 300°F (150°C) for 35–45 minutes, until the edges are set but the center still has a slight jiggle when you gently nudge the pan.

Remove the pan from the oven and place it on a wire rack. Let the bars cool at room temperature for about 1–1 1/2 hours. Transfer the pan to the refrigerator (uncovered) and chill for at least 4 hours, preferably overnight, until fully set.

Once fully chilled, use the parchment overhang to lift the slab out of the pan onto a cutting board. Use a long, sharp knife to cut into 16 large bars or up to 24 smaller bars, wiping the knife with a warm, damp cloth between cuts for the cleanest slices. Top with powdered sugar, whipped cream, crushed cookies, or a drizzle of caramel sauce, if desired. Serve cold or slightly cool.