Make the cake: Preheat the oven to 350°F. Line a 9 × 13-inch baking pan with parchment paper. Cream together the sugar and butter for 2 minutes. Add the buttermilk, vanilla, and egg and mix on low speed until blended. Mash the bananas slightly, add them to the bowl, and mix well on low speed.

In a separate bowl, whisk together the flour, baking powder, and salt. Mix the dry ingredients into the wet ones just until incorporated. Spread the cake batter onto the baking pan in an even layer.

Bake the cake for 25 to 30 minutes, or until a toothpick inserted into the center comes out clean. Remove from the oven and allow to cool completely.

Make the pudding: Whisk together the granulated sugar, cornstarch, salt, and vanilla bean seeds in a medium saucepan. Whisk in the egg yolks until well combined. Slowly pour in the milk, whisking to incorporate it. Cook the mixture over medium-low heat until it thickens, about 10 to 15 minutes. Remove from the heat and whisk in the butter one piece at a time, making sure each piece is incorporated before adding the next. Cover the top of the pudding with plastic wrap and refrigerate until cool, 1½ to 2 hours.

Using the top of an 8-ounce jar as a guide, cut 10 circles from the cake. Fit the circles into the bottoms of ten 8-ounce jars. Slice the ripe bananas ¼ inch thick and line the sides of the jars with the banana slices pressed up against the glass, two slices deep. Pour the pudding into the jars to cover the bananas.

In a medium bowl, beat together the heavy cream and the confectioners’ sugar until stiff peaks form. Spoon the whipped cream over the pudding. Refrigerate until ready to serve.