Blackberry and Apple Cake

Name: Blackberry and Apple Cake
Ingredients: 3⁄4 cup softened unsalted butter, plus more for greasing pan; 1 1⁄2 lb. fresh blackberries (about 6 cups); 1 tbsp. dark brown sugar; 3 granny smith apples, cored, peeled, and quartered; 1⁄3 cup apple brandy, such as calvados; 2 1⁄2 cups cake flour; 2 1⁄4 tsp. baking powder; 1 tsp. ground cinnamon; 1⁄2 tsp. fine salt; 3⁄4 cup milk; 1 1⁄2 tsp. vanilla extract; Zest of 1 lemon; 1 cup plus 2 tbsp. superfine sugar; 4 eggs; Crème fraîche, for garnish (optional)