Preheat your oven to 350°F (175°C).
Peel, core, and slice the apples into thin slices. Place the apple slices in a mixing bowl and drizzle with lemon juice to prevent browning.
In another mixing bowl, combine 1 cup of granulated sugar, 1/4 cup of brown sugar, 1 cup of all-purpose flour, 1 teaspoon of baking powder, 1 teaspoon of ground cinnamon, and 1/4 teaspoon of salt. Mix well to ensure all ingredients are evenly distributed.
Add the melted butter, milk, and vanilla extract to the dry ingredients. Stir until the batter is smooth and well combined.
Pour the batter into the greased 9x13 inch baking dish. Evenly distribute the apple slices on top of the batter. The apples will sink slightly as they bake, creating a delicious layer of fruit within the cobbler.
Place the baking dish in the preheated oven and bake for 45-50 minutes, or until the cobbler is golden brown and a toothpick inserted into the center comes out clean.
Allow the cobbler to cool for about 10 minutes before serving. Serve warm, optionally with a scoop of vanilla ice cream or a dollop of whipped cream for extra indulgence.