Wash, peel, and core the apples. Cut the apples into medium thin slices, about 1 inch thick. Place the apples in a large bowl. Add the brown sugar and cinnamon to the apples and toss lightly to mix.
Put the stick of butter in a baking dish in place in the oven for about 3 minutes to melt; remove from the oven. Add the apple mixture to the butter and put back in the oven for about 10 minutes.
While the apples are baking, mix together the flour, white sugar, baking powder, milk, and vanilla extract. Pour the flour batter into the baking dish on top of the the apple mixture.
Place the baking dish in the oven and bake about 40-45 minutes, until brown. Remove from the oven and let cool for about 15 minutes. Serve with ice cream.
Notes
I use a 2 1/2-quart oval dish for this cobbler. If you use a smaller pan, allow extra time in the oven.