Fresh Fig and Almond Cake

For the cake: 1 1/2 cups all-purpose flour 1 cup whole wheat flour 2 teaspoons baking powder 1/2 teaspoon baking soda 1/2 teaspoon salt 1/4 teaspoon ground cardamom 1/2 cup granulated sugar 2 large eggs 1 1/2 cups buttermilk 1/4 cup unsalted butter, melted and slightly cooled 1 teaspoon pure vanilla extract 1/2 teaspoon pure…