Preheat the oven to 400°F (205°C).
Peel and cut the peaches into thin wedges to make about 2 cups and transfer to a microwave-safe dish.
Add the brown sugar, lemon juice, ground cinnamon, vanilla extract, and salt over the peaches and toss to coat evenly. Place the butter on top and microwave for about 4 minutes, until the peaches have released their juice and the mixture has thickened slightly. Stir well and set aside to cool.
Add the cream cheese and mascarpone to a bowl and mix until smooth and creamy.
Spread the cheese mixture generously over the flatbread, leaving the edges clear. Arrange the cooked peach slices on top in an even layer.
Bake for 10 minutes until the edges are golden brown. Let cool for a few minutes, garnish with fresh mint leaves, and serve.