Preparation

Make the cake

• In a 2-quart saucepan, cook the butter over medium heat, swirling every few seconds, until melted and the milk solids at the bottom of the pan turn dark brown, about 5 minutes. Immediately scrape the browned butter and milk solids into a shallow bowl. Refrigerate until softly set, about 1 hour.
• Position a rack in the center of the oven and heat the oven to 350°F. Butter three 9-inch round cake pans, line the bottoms with parchment, butter the parchment, and flour the pans.
• In a medium bowl, whisk together the flour, baking powder, salt, cinnamon, and baking soda. In a separate bowl or measuring cup, whisk together the mashed bananas and buttermilk.
• In a large bowl, beat the browned butter and brown sugar with an electric mixer (hand-held, or a stand mixer fitted with the paddle attachment) on medium speed until light and fluffy, about 4 minutes. Add the eggs one at a time, beating well after each addition. Reduce the speed to low and alternately add the flour and banana mixtures in three additions each. Fold in the pecans with a spatula.
• Divide the batter evenly among the prepared pans, and smooth with the spatula. Tap the pans on the counter to break any air bubbles.
• Bake the cakes, rotating and switching positions halfway through baking, until a tester inserted in the centers comes out clean, about 35 minutes. Let the cakes cool in the pans on racks for 10 minutes. Turn the cakes out onto the racks, remove the parchment, and cool completely.

Make the ganache

• In a 1-quart saucepan, cook the butter over medium heat, swirling every few seconds, until melted and the milk solids at the bottom of the pan turn dark brown, about 5 minutes. Immediately scrape the browned butter and milk solids into a medium metal bowl. Add the chocolate and kosher salt.
• Bring the cream to a boil in the same pot over medium heat, and then pour over the chocolate and butter. Let stand 2 minutes, and then whisk until smooth. Cool at room temperature, stirring every 15 minutes, until thickened and spreadable, about 1 hour.

Assemble the cake

• Put one of the cake layers on a cake plate and top with 3/4 cup ganache, spreading it to the edge with an offset spatula. Add another cake layer and spread with another 3/4 cup ganache. Add the third cake layer and spread the remaining ganache over the top and side of the cake. Sprinkle the top with a few pinches of flaky salt. The cake will keep at room temperature, covered with a dome, for up to 24 hours.