Preheat the oven to 400°F.
Add peaches, brown sugar, cornstarch, vanilla extract, cinnamon, and salt to a saucepan over medium heat and stir well.
Once the mixture begins to bubble, reduce heat to low and cook for 10 to 15 minutes until the peaches soften and the filling thickens slightly.
In a separate bowl, combine butter, flour, granulated sugar, cinnamon, and salt until crumbly.
Fill two ramekins with the peach filling.
Top each ramekin evenly with the crumble topping.
Place ramekins on a baking sheet and bake for 15 to 20 minutes until the topping is lightly browned and the filling bubbles.
Let the cobblers cool for 5 minutes before serving.