Preheat oven to 375°F and line an 8-inch square baking pan with parchment paper, leaving some hanging over the edges of the pan. Set aside.
In a food processor, pulse the graham crackers until they become fine crumbs. Add melted butter, ¼ cup of brown sugar, and salt. Process until incorporated and the ingredients become like wet sand.
Pour crumb mixture into prepared pan. Press evenly over the bottom and about 1 inch up the sides of the pan. Bake until golden and fragrant, about 10 minutes. Transfer pan to wire rack to cool slightly and reduce the oven temperature to 325°F.
In a medium bowl, whisk together the pumpkin, 1 egg, 2 tablespoons of brown sugar, 1 tablespoon of flour, pumpkin pie spice, and ½ teaspoon of vanilla bean paste. Set aside.
Wipe out the food processor bowl with a paper towel. Add the cream cheese, granulated sugar, 2 eggs, sour cream, 1 tablespoon of flour, and 1 teaspoon of vanilla bean paste. Process until completely smooth (about 1 minute). Scrape down the sides of the bowl and process again for 30 seconds.
Spread cheesecake mixture evenly over warm crust. Drop spoonfuls of pumpkin mixture over cheesecake mixture. Using a butter knife, lightly swirl the mixtures together, being careful not to scrape the crust. Bake until cheesecake jiggles slightly in the center when pan is nudged, 50-55 minutes.
Cool completely in pan on a wire rack. Chill at least 4 hours or up to overnight before cutting into bars.