In a small bowl, mix together mascarpone cheese and jam.
In a larger bowl, whisk together eggs, milk, vanilla extract, ground cinnamon, and salt.
Spread mascarpone and jam mixture evenly on four pieces of challah, leaving a little bit of space around the edges. Top with remaining bread slices.
Melt 1 tablespoon butter in a large pan over medium heat. Meanwhile, dip sandwiches in batter and hold for about 5 seconds. Flip and soak on other side for 5 seconds. Quickly transfer the sandwich to the pan and cook on each side for about 2-3 minutes, until nicely browned.
Transfer stuffed french toast to plate and top with maple syrup, blackberries, and more jam.