Preheat your oven to 375°F (190°C). Grease a 9x9-inch baking dish or a similar-sized baking dish.

In a medium saucepan, melt the butter over low heat. Remove from heat and set aside.

In a mixing bowl, combine the flour, sugar, baking powder, salt, and cinnamon (if using). Stir until well combined.

Gradually pour in the milk and vanilla extract, stirring continuously, until the batter is smooth and free of lumps.

Pour the melted butter into the greased baking dish, spreading it evenly across the bottom.

Arrange the sliced peaches on top of the melted butter in a single layer.

Pour the batter over the peaches, spreading it evenly to cover them.

Place the baking dish in the preheated oven and bake for about 40-45 minutes or until the top is golden brown and the cobbler is bubbling.

Remove the cobbler from the oven and let it cool for a few minutes before serving.

Serve the peach cobbler warm with a scoop of vanilla ice cream if desired.