Preheat the oven to 350°F (175°C). Grease a 9- or 10-inch round cake pan or springform pan and line with parchment paper.
Prepare the crust: In a mixing bowl, combine the yellow cake mix, 1 egg, and 4 tablespoons melted butter. Mix until smooth. Press evenly into the bottom of the prepared pan.
Make the pumpkin filling: In a separate bowl, blend pumpkin puree, softened cream cheese, 3 eggs, ½ cup melted butter, brown sugar, vanilla, cinnamon, nutmeg, and ginger. Mix on low until fully combined, scraping the sides of the bowl as needed.
Assemble the cake: Pour the pumpkin filling over the cake crust, spreading evenly.
Bake: Place in the preheated oven for 40–50 minutes, until the edges are set and the top is lightly golden. The center should remain slightly gooey.
Cool: Allow the cake to rest for at least 10 minutes before slicing.