Preheat oven to 350°F / 177°C. Lightly grease a 9x13 baking pan.
Make cake: In a small bowl, combine flour, baking soda, and salt. Set aside.
Using a stand mixer fitted with the paddle attachment or a handheld mixer, beat together the butter (for the cake) and white sugar until very light and fluffy, 3 to 4 minutes. Add eggs one at a time, mixing well after each addition. Add vanilla and mix until evenly combined.
Alternate adding the half the dry ingredients and half the buttermilk, mixing after each addition, until everything is evenly combined. Add mashed bananas and mix on low just until even. (Do not over mix.)
Spread cake batter out in prepared baking pan.
Bake until cake is set in the middle, 55 to 65 minutes. (If using a metal pan, it should finish on the lower end of the range; if using a glass or ceramic pan, it will need closer to the higher end.)
Make cream cheese frosting: Using a stand mixer fitted with the whisk attachment or handheld mixer, beat the butter and cream cheese on high until smooth and even, 2 to 3 minutes. Add 2 tablespoon milk, vanilla, and powdered sugar and mix on low to combine everything. Switch to high and beat until very smooth, 2 minutes more. If the frosting is too thick to spread, add additional milk a little at a time. Transfer to a bowl.
Make chocolate frosting: Wipe out the bowl used to make the cream cheese frosting. Combine butter, cocoa powder, honey, and vanilla. Beat on high until very smooth and creamy. Add powdered sugar and 2 tablespoon milk. Continue mixing until evenly combined. Continue beating, adding extra milk as needed, until the frosting is a smooth, thick but spreadable consistency.
Wait until cake is completely cool to slice it in half across the shortest side, dividing it into two even pieces. (Do not frost the cake if it is warm or the frosting will melt.)
If the top of the cake is rounded, use a serrated knife to even it out.
Place one of the cake squares on a serving platter or cake stand. Spread a layer of cream cheese frosting on top.
Place the second square of cake on top of the cream cheese frosting. Frost the entire outside of the cake with an even layer of chocolate frosting. Refrigerate for up to 12 hours.
Slice and serve!