Preheat your oven to 375°F (190°C).
In a large mixing bowl, combine the sliced peaches with brown sugar, corn starch (or flour), bourbon (if using), vanilla extract, ground ginger, ground allspice, and ground cardamom. Toss the ingredients until the peaches are well coated.
Transfer the peach mixture into a greased baking dish, spreading it out evenly.
In another bowl, prepare the topping. Mix melted butter, brown sugar, egg, and vanilla extract until well combined. Add flour, baking powder, and salt. Stir until a dough forms.
Drop spoonfuls of the topping evenly over the peach mixture.
Sprinkle granulated sugar over the topping.
Bake in the preheated oven for about 40-45 minutes or until the topping is golden brown, and the peach filling is bubbly.
Allow the cobbler to cool for a few minutes before serving.
Serve warm with a scoop of vanilla ice cream on top. Optionally, sprinkle ground vanilla bean for an extra burst of flavor.