2 cups mashed ripe banana (about 5 large bananas)
1 1/2 cups firmly packed dark brown sugar
2 1/4 cups granulated sugar, divided
4 large eggs, room temperature
1 cup canola oil
1 cup sour cream, room temperature
2 1/2 teaspoons vanilla extract
4 cups all-purpose flour
2 teaspoons baking soda
1 1/4 teaspoons kosher salt, divided
1 cup spiced rum
6 large egg whites, room temperature
1/4 teaspoon cream of tartar
1/4 teaspoon rum extract
3 large ripe bananas (about 1 1/4 pounds), cut into 1/3-inch-thick slices
Preheat oven to 350°. Spray 2 (9-inch) round cake pans with baking spray with flour; line bottoms with parchment paper.
In the bowl of a stand mixer fitted with the paddle attachment, beat mashed banana, brown sugar, 1 cup granulated sugar, eggs, oil, sour cream, and vanilla at medium speed until combined, 1 to 2 minutes, stopping to scrape sides of bowl.
In a large bowl, whisk together flour, baking soda, and 1 teaspoon salt. With mixer on low speed, gradually add flour mixture to banana mixture, beating just until combined, 1 to 2 minutes, stopping to scrape sides of bowl. Divide batter between prepared pans. Forcefully tap pans on counter several times to release any air bubbles.
Bake on center rack of the oven until a wooden pick inserted in center comes out clean, 35 to 40 minutes. Let cool in pans for 15 minutes. Remove from pans, and let cool completely on wire racks. Using a serrated knife, level top of cake layers. Poke each layer several times with a fork or wooden pick. Brush cake layers with rum.
In the bowl of a stand mixer, whisk together egg whites, cream of tartar, remaining 1 1/4 cups granulated sugar, and remaining 1/4 teaspoon salt. Place mixer bowl over a saucepan of simmering water. Heat egg white mixture, stirring constantly, until a candy thermometer registers 160°, 10 to 20 minutes. Remove from heat; carefully return bowl to stand mixer. Using the whisk attachment, beat at high speed until bowl returns to room temperature and meringue forms glossy, stiff peaks, about 10 minutes. Beat in rum extract.
Place one cake layer on a serving plate. Arrange banana slices in a single, flat layer on top of cake. Place about 1 1/4 cups meringue in a large piping bag fitted with a medium, round tip; pipe an even circular layer over bananas, and smooth using a small offset spatula. Place remaining cake layer on top of meringue. Gently press down on layer to line meringue up with bananas, if necessary. Top with remaining meringue. Using the back of a spoon or a large offset spatula, decoratively spread meringue up to 1/4-inch from edge. Using a kitchen torch, brown meringue. Freeze for 30 to 40 minutes before serving.