Preheat the oven to 350°F. Lightly grease a baking pan and set it aside. Peel the apples, remove the cores, and slice the fruit into pieces approximately ¼ inch thick.

Place the brown sugar, apple juice or water, cornstarch, lemon juice, vanilla extract, cinnamon, nutmeg, and salt in a saucepan. Whisk thoroughly until the cornstarch has dissolved and the mixture is smooth.

Set the saucepan over medium heat and bring the liquid to a gentle simmer. Add the sliced apples and cook for 3–5 minutes, stirring carefully, until the fruit begins to soften and the surrounding liquid thickens slightly. Avoid cooking the apples completely, as they will continue to soften in the oven.

In a separate mixing bowl, whisk together the all-purpose flour, granulated sugar, baking powder, and salt until evenly distributed.

Combine the room-temperature milk with the melted, slightly cooled butter in a small bowl or measuring jug.

Transfer the warm apple mixture to the prepared baking pan and spread it into an even layer.

Pour the milk-and-butter mixture into the dry ingredients. Stir gently with a spatula only until a batter forms. Do not overmix; a few small lumps will help preserve the topping’s tender, rustic consistency.

Distribute the batter evenly over the apple filling. The mixture may appear relatively thin at this stage, but it will rise and firm as it bakes.

Dust the surface with approximately ¼ teaspoon ground cinnamon.

Bake for 38–40 minutes, or until the topping is golden brown and a toothpick inserted into the baked batter comes out clean. The apple filling should be visibly bubbling around the edges.

Remove the cobbler from the oven and allow it to rest for 15 minutes before serving. This cooling period helps the filling thicken while keeping the apples warm and succulent.