In a small bowl, combine the sliced peaches, 2.5 tablespoons brown sugar, and 0.5 teaspoon cinnamon. Stir well to coat the peaches evenly with the sugar and spice. Microwave this mixture on high for 1.5 minutes, then stir to ensure even cooking and to help the peaches release their juices. The filling should be warm and slightly syrupy at this point.

In another small bowl, whisk together the flour, milk, 0.5 teaspoon cinnamon, ground nutmeg, 1 tablespoon sugar, vanilla essence, baking powder, and salt until you have a smooth batter with no lumps. I always use King Arthur all-purpose flour because it gives the topping better structure and a more tender crumb. The batter should be thick but pourable—similar to pancake batter.

Melt 1 tablespoon of butter in a microwave-safe mug or ramekin for about 30 seconds. Pour the warm peach filling from Step 1 (including all the juices) directly over the melted butter. Then carefully pour the batter from Step 2 over the peaches, spreading it gently with a spoon to cover the filling—it doesn't need to be perfectly even since it will rise and fill in gaps as it cooks. Microwave on high for 1 minute.

Remove the mug from the microwave carefully—it will be hot! Sprinkle 1 tablespoon of brown sugar evenly over the top of the cobbler. I like brown sugar here because it adds a deeper, caramel-like chew to the crust as it cooks slightly from the residual heat. Let the cobbler rest for 1-2 minutes to cool slightly before serving, which allows the topping to set a bit and makes it easier to enjoy.