Step 1: In a large mixing bowl, combine the all-purpose flour, granulated sugar, softened unsalted butter, eggs, baking powder, and vanilla extract. Beat until the mixture is well combined and smooth. Gently fold in the peeled and diced apples. Pour the prepared batter evenly into a greased 9-inch round baking dish or an 8x8 inch square baking dish.
Step 2: Preheat your oven to 350°F (175°C). Place the baking dish with the cake batter into the preheated oven and bake for 30-35 minutes, or until a toothpick inserted into the center of the cake comes out clean, indicating it's fully cooked through.
Step 3: While the cake is baking, prepare your luscious caramel drizzle. In a small saucepan, combine 1/2 cup granulated sugar, 1/4 cup unsalted butter, and heavy cream. Cook this mixture over medium heat, stirring continuously, until the sugar completely dissolves and the caramel becomes smooth and slightly thickened. Be careful not to burn the sugar.
Step 4: Once the cake is out of the oven, immediately drizzle the warm caramel sauce generously over the entire baked cake. If desired, sprinkle with chopped nuts (almonds or walnuts work great) and granola for a delightful crunch. For an extra touch of beauty, arrange fresh apple slices on top and dust with powdered sugar. Serve your divine Swedish Apple Cake warm and enjoy every heavenly bite!