Swedish Apple Cake (Äppelkaka)

Name: Swedish Apple Cake (Äppelkaka)
Prep time: 30 min
Cook time: 40 min
Total time: 1 h 10 min
Cuisine: European
Ingredients: 3 medium granny smith apples (peeled, cored and cut into ½ inch thick wedges (about 1 pound)); 2 tablespoons unsalted butter; 3 tablespoons packed light brown sugar; 1 teaspoon cinnamon; 1 cup all-purpose flour; 1 teaspoon baking powder; ½ teaspoon fine salt; ½ teaspoon ground cardamom; ¾ cup granulated sugar; ¼ cup packed light brown sugar; 2 large eggs; 6 tablespoons unsalted butter (melted and cooled); ¼ cup sour cream; 1 teaspoon vanilla