Combine raspberry jam, Dijon mustard, and rosemary in a small bowl.

Lay out brioche bread slices.

Spread the jam mixture evenly over the bread slices.

Add a slice of Swiss cheese to each bread slice.

Top the cheese with two slices of prosciutto cotto.

Assemble the sandwiches.

Whisk eggs in a medium bowl.

Add heavy cream and salt to the eggs and whisk to combine.

Heat olive oil in a large skillet over medium heat.

Dip each sandwich in the egg batter, coating both sides.

Place the dipped sandwich into the hot skillet.

Repeat with remaining sandwiches.

Cover the skillet and cook each side until golden brown (3-4 minutes per side).

Flip the sandwiches and continue cooking until the cheese is melted and golden brown.

Sprinkle one side of each sandwich with powdered sugar.

Serve warm.