Buttermilk Banana Cake

Name: Buttermilk Banana Cake
Ingredients: ½ cup (1 stick) unsalted butter, room temperature, plus more for pan; 2 cups (250 g) all-purpose flour; ½ tsp. baking powder; ½ tsp. baking soda; ½ tsp. Diamond Crystal or ¼ tsp. Morton kosher salt, plus more; ½ tsp. ground cardamom, plus more for sprinkling; ¾ cup (150 g) granulated sugar; ¾ cup (packed; 150 g) light brown sugar; 2 large eggs, room temperature; 1½ tsp. vanilla extract, divided; 2 ripe bananas, peeled, flesh finely mashed; 1¼ cups buttermilk, room temperature, divided; 1½ cups (165 g) powdered sugar; Flaky sea salt