Preheat the oven to 375 degrees F.
In a 9x13 baking dish, mix together the strawberries and blueberries. Sprinkle with the sugar and flour, then sprinkle on the lemon juice. Toss everything together well until the sugar is moistened and all the berries are covered. Let sit while you make the topping.
In a small bowl, whisk together the flour, sugar, baking powder and salt.
Place the melted butter in a large bowl. Mix in the mascarpone cheese - this will take a minute to come together. You can use a whisk, spatula or wooden spoon. Mix in the heavy cream and vanilla extract until combined.
Mix in the dry ingredients until fully combined. Drop the batter by the spoonful all over the berries. Sprinkle the batter with a little bit of coarse turbinado sugar.
Bake for 55 to 60 minutes, or until the topping is golden brown and cooked through. Let cool slightly before serving with ice cream.