1.) Preheat the oven to 350°F (180°C). Spray a 13×9-inch baking pan with cooking spray. Line pan with parchment paper, letting excess extend over sides of pan; spray pan again.
2.) In a large bowl, whisk together brown sugar, granulated sugar, 6 tablespoons melted butter, and 2 eggs. Add flour, baking powder, and salt, whisking until smooth. Spread into bottom of prepared pan; set aside.
3.) In the bowl of a stand mixer fitted with the paddle attachment, beat cream cheese at medium-low speed until smooth. Add pumpkin, and beat until combined, 2 to 3 minutes. Add rum, remaining 3 eggs, and remaining 1⁄2 cup melted butter, beating until smooth. Gradually add confectioners’ sugar, cinnamon, ginger, nutmeg, allspice, and cloves, beating until well combined. Pour over the cake base, and gently shake the pan back and forth to help spread in an even layer; smooth with an offset spatula, if necessary.
4.) Bake until the center is slightly set, about 40 minutes. (Top will look dry and the center will jiggle together with the rest of the pan.) Let cool completely in the pan. (Center will sink slightly.) Using excess parchment as handles, remove from pan. Dust with confectioners’ sugar, if desired.