Peel, pit, and slice the peaches into 1/2-inch thick wedges. In a small bowl, combine the brown sugar, cornstarch, cinnamon, almond essence, and nutmeg. Add the peach slices to this mixture and toss gently until all the fruit is evenly coated with the spice blend. This coating will thicken as it cooks and create a delicious filling. Divide the peach mixture evenly between two ramekins, spreading it in an even layer on the bottom.
While the peaches are being prepared, melt the butter and let it cool slightly. In a separate bowl, whisk together the flour, sugar, baking powder, and salt. Pour the melted butter into the dry ingredients and stir until just combined into a thick, biscuit-like batter. I like to use a fork to break up any lumps so the topping bakes evenly without dense pockets.
Divide the cobbler topping equally between the two ramekins, spooning it over the peach filling. Don't spread it completely smooth—I let it stay slightly lumpy on top for a more rustic, appealing cobbler texture. Place both ramekins in the air fryer basket and cook at 350°F for 9-11 minutes, until the topping is golden brown and a toothpick inserted into the topping comes out clean.
Remove the ramekins from the air fryer and let them cool for 5 minutes before serving. This allows the filling to set slightly while the cobbler is still warm and delicious.