Preheat the oven to 350°F. Lightly grease a muffin pan or individual tart molds. Add 1 tablespoon of butter and a little of the caramel sugar to the bottom of each muffin cup. Wash and peel the apples if desired, remove the cores, and slice them thinly. Arrange the apple slices in overlapping layers inside each cup, creating a flower-like pattern. Thin, evenly cut slices will soften more consistently and help give the finished tarts their pretty appearance.

In a large bowl, beat the eggs with 1/2 cup sugar until the mixture looks lighter and slightly fluffy. Stir in the warm milk, melted butter, and vanilla extract until combined. In a separate bowl, whisk together the flour, baking powder, salt, and optional cinnamon. Gradually add the dry ingredients to the wet mixture, stirring gently until a smooth batter forms. Avoid overmixing. Spoon the batter over the arranged apples, filling each cup about two-thirds full to leave room for the cakes to rise.

Place the muffin pan in the preheated oven and bake for 20–25 minutes, or until the tops are lightly golden and a toothpick inserted into the cake comes out clean. The exact baking time may vary depending on your pan and the size of the portions. Check the center of a cake for doneness rather than relying on color alone.

Let the tarts rest briefly after baking. Carefully loosen the edges with a small knife, then invert them while the caramel is still warm and fluid. Use oven mitts when handling the pan, and take care not to touch the hot caramel, which can cause serious burns. Allow the tarts to cool until warm before serving. Enjoy them as they are or add a spoonful of whipped cream for an extra-special finish.