For the cake:

6 tablespoons unsalted butter, divided
3/4 cup dark brown sugar
6 tablespoons dark rum
3 ripe bananas, sliced into 1 1/2-inch chunks (about 2 cups of banana pieces)
2 large eggs, at room temperature
1 1/2 teaspoons pure vanilla extract
2 cups cake flour
2 teaspoons baking powder
3/4 teaspoon salt

For the streusel:

7 tablespoons all-purpose flour
1/3 cup granulated sugar
4 tablespoons unsalted butter, softened