Preheat oven to 350°F (175°C).

Place butter stick in a baking pan (e.g., 9x13 inch) and melt in the preheating oven.

Remove the pan from the oven and pour the sliced peaches (with their juice) into the pan over the melted butter.

In a separate bowl, combine flour, sugar, and baking powder.

In a separate small bowl or measuring cup, add vanilla to the milk.

Pour the milk and vanilla mixture over the dry ingredients.

Gently mix the wet and dry ingredients together until just combined. Do not overmix.

Pour the batter evenly over the peaches in the baking pan.

Do not stir the batter and peaches together. This is important for the cobbler's texture.

Bake in the preheated oven for 35 to 45 minutes, or until the crust is golden brown and the peaches are bubbly.

Remove from the oven and let cool slightly before serving.

Optional: Sprinkle the crust lightly with granulated sugar while still warm.