Preheat oven to 350° F and line a 9x13” pan with parchment paper.
Place butter in a small saucepan and set over medium heat, swirling regularly, until it begins to foam, about 6 minutes. Butter should be fragrant and nutty, with little brown flecks. Remove from heat and let cool to room temperature.
In a small bowl, whisk together flour, baking powder, baking soda, cardamom, cinnamon, and kosher salt. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, combine browned butter, brown sugar, and granulated sugar. Mix on medium speed until smooth and reaches the consistency of very wet sand.
Add the eggs, one at a time, mixing after each addition until homogenous, followed by the vanilla extract and the bananas.
With the mixer on low speed, gradually add dry ingredients in three additions, alternating with the sour cream beginning and ending with the dry ingredients. When the last of the dry ingredients have been added, mix until just combined and no dry streaks remain.
Transfer batter to prepared pan and smooth into an even layer with a small offset spatula. Bake for 20-25 minutes, rotating the pan halfway through the baking time, until cake is golden brown and beginning to pull away from the sides of the pan. A knife or toothpick inserted into the center of the cake should come out clean. Let cool completely before frosting.
To make the frosting: In the bowl of a stand mixer fitted with the whisk attachment combine sour cream and heavy cream. Whip, starting on low speed and gradually increasing speed until cream is thickened and soft peaks form. Add powdered sugar, vanilla extract, honey and salt, and continue whipping on medium-high speed until medium peaks form, or the consistency of whipped cream. Scoop and swirl frosting over the cooled banana cake and serve immediately.