Combine first 4 ingredients in a small bowl; stir in 1/4 cup melted butter. Use fingers to pinch streusel into big clumps. Set aside.
Beat 1 cup butter at medium speed with an electric mixer about 2 minutes or until creamy. Gradually add 2 cups each granulated and dark brown sugar, beating at medium speed 5 to 7 minutes. Add eggs, 1 at a time, beating just until yellow disappears.
Stir together pumpkin and 1/4 cup rum in a bowl. Combine flour and next 7 ingredients in a medium bowl. Add flour mixture to butter mixture alternately with pumpkin, beginning and ending with flour.
Pour half of batter into a well-greased and floured 12-cup Bundt pan. (We recommend greasing pan with shortening.) Sprinkle batter with streusel; top with remaining batter.
Bake at 325° for 1 hour and 28 minutes or until a long wooden pick inserted in center comes out clean. Cool in pan on a wire rack 10 minutes; remove from pan, and let cool completely.
Combine 3/4 cup brown sugar, whipping cream, and 1/4 cup unsalted butter in a medium saucepan. Cook, stirring constantly, over medium-low heat, until butter melts and sugar dissolves. Increase heat to medium-high, and bring to a boil. Boil 3 minutes. Remove from heat, and stir in 1 tsp. rum.
Place powdered sugar in a bowl; pour brown sugar mixture over powdered sugar, stirring with a wire whisk 1 minute or until smooth. Let cool 20 to 25 minutes or until lukewarm. Spoon icing over cooled cake, and let stand until icing is firm.