Step 1

Preheat oven to 350°F. Place butter in bowl of a stand mixer fitted with a paddle attachment, or place in a large bowl and use an electric mixer. Beat butter on medium speed until creamy, then gradually beat in granulated sugar and brown sugar until thoroughly combined, 1 to 2 minutes, stopping to scrape down sides of bowl as needed. Add eggs, 1 at a time, beating just until blended after each addition, scraping down sides and bottom of bowl between additions. Add mashed bananas and vanilla, and beat on low speed just until combined.

Step 2

Stir together flour, baking soda, cinnamon, salt, and nutmeg in a medium bowl. Gradually add flour mixture to butter mixture, beating on low speed just until blended and no dry ingredients remain, stopping to scrape down sides of bowl as needed. Lightly coat bottom and sides of a 15- x 10-inch rimmed baking sheet with butter and lightly dust with flour; spread batter evenly into prepared pan. Bake in preheated oven 12 minutes; remove from oven. (Cake will not be completely cooked.)

Step 3

Meanwhile, make streusel: Stir together walnuts, brown sugar, flour, oats, melted butter, and salt in a medium bowl until well combined. Sprinkle mixture in an even layer over cake. Return cake to oven, and bake at 350°F until a wooden pick inserted in center comes out clean, 8 to 12 minutes more. Cool completely in pan on a wire rack, about 1 hour.

Step 4

Stir together rum and powdered sugar in a small bowl. Stir in heavy cream, 1 tsp. at a time, until desired consistency, thick but pourable. Drizzle rum glaze evenly over cooled cake. Cut cake into about 3- x 5-inch pieces, and serve.