Preheat oven to 350°. Butter a 9-in. square pan and line the bottom with parchment paper.
In a small saucepan over medium heat, melt butter. Whisk in brown sugar until blended. Remove from heat and whisk in rum. Pour mixture into prepared pan, evenly covering the bottom.
In a small bowl, combine cranberries and walnuts; arrange evenly over brown sugar mixture.
In a large bowl with a mixer on medium speed, beat eggs, pumpkin, oil, and granulated sugar until smooth. In another bowl, stir together flour, baking powder, cinnamon, and salt. Stir flour mixture into pumpkin mixture. Spread batter evenly over cranberries and walnuts.
Bake until a skewer inserted in the center of cake comes out clean, 35 to 45 minutes. Transfer to a wire rack and let cool 10 minutes in pan. Run a thin-bladed knife between cake and sides of pan, then invert cake onto a serving platter. Remove pan and parchment, and let cool at least 20 minutes. Serve slightly warm or cool, with whipped cream.
Note: Nutritional analysis is per serving.