Preheat oven to 325°F (163°C). Line a 9x9-inch baking pan with parchment paper, leaving a 2-inch overhang on two opposite sides. Grease lightly with butter or nonstick spray.

In a medium bowl, whisk graham cracker crumbs, 1/4 cup sugar, 1/2 teaspoon ginger, 1/2 teaspoon cinnamon, 1/4 teaspoon cloves, and salt.

In a small bowl, stir the melted butter and 2 tablespoons molasses together. Pour over the dry crumb mixture and toss with a fork until evenly moistened and looks like wet sand. Press firmly into the prepared pan using a flat-bottomed measuring cup.

Bake the crust for 10 minutes. Set it aside to cool slightly while you make the filling.

In a large bowl, beat the softened cream cheese with an electric mixer on medium speed until smooth, about 2 minutes. Scrape down the sides, add 1/2 cup sugar, and beat for 1 minute until light and fluffy.

Add the eggs one at a time, beating on low after each addition just until incorporated. Mix in the vanilla and sour cream on low until combined. Gently fold in the flour with a spatula until no white streaks remain.

In a small bowl, whisk together 2 tablespoons molasses, 1/2 teaspoon ginger, 1/4 teaspoon cinnamon, and a pinch of nutmeg.

Pour the cheesecake filling over the crust and spread it evenly. Drop small spoonfuls of the molasses mixture on top, then gently swirl through with a knife or toothpick in 5 to 6 figure-eight motions.

Bake for 35 to 40 minutes, until the edges are set and the center jiggles slightly when the pan is gently shaken. Turn off the oven, crack the door open, and let the bars rest inside for 10 minutes.

Remove the pan from the oven and cool completely on a wire rack, about 1 hour. Cover with plastic wrap and refrigerate for at least 4 hours, preferably overnight.

Lift the chilled slab out using the parchment overhang. Transfer to a cutting board and slice into 16 squares (4 by 4) with a sharp knife, wiping the blade clean between cuts.