Spread 2 Tbsp. mascarpone cheese on each of the 4 bread slices.
Divide raspberries and blueberries equally and place on top of the mascarpone cheese.
Divide the jam equally and spread evenly over the 4 remaining slices of bread.
Cover each mascarpone-covered slice with a jam-covered slice and press the sandwiches together. Butter both sides of each sandwich.
Preheat a panini grill pan over medium heat for 3 - 4 minutes.
Arrange the sandwiches on the hot grill pan. Place the panini press on top of the sandwiches and cook for 1 - 1 1⁄2 minutes or until golden and crispy.
Carefully flip each sandwich, replace the panini press and cook for 1 - 1 1⁄2 minutes or until golden on the reverse side.
Transfer the sandwiches to a plate.