Heat the oven to 375 degrees F.
Set out the puff pastry sheet to thaw for 15 minutes. When thawed unroll the pastry on a flat surface like a cutting board to flatten it.
With a cheese shredder, shred the cheese over a plate, or measure out the preshredded cheese. On a small cutting board, pull the fresh rosemary off the stem and then chop the leaves.
Spread the jam over the pastry sheets with a spoon or a knife. You just need a thin layer, so don't feel you have to use the whole ⅓ cup. Leave some space at the end of the roll without jam or cheese.
Sprinkle the parmesan cheese and chopped rosemary over the jam.
Break the egg into a small bowl, and beat with a fork.
Starting with the short side of the dough, roll up the pastry sheet into a tight roll. Brush the end with the egg wash and then continue rolling up the dough. The egg wash will seal the pastry together so I won't come unrolled.
Optional - brush more of the egg wash over the top of the roll. This will add some shine to the baked pastry and make it more golden brown.
With a serrated knife, cut the roll into ¼" slices and place the slices on the silicone mat-lined baking sheet.
Bake for 10-12 minutes or until golden brown.
Serve warm or at room temperature.
Store leftover rolls in an airtight container in the refrigerator for several days. To reheat the rolls, wrap in aluminum foil bake in a 300 degrees until warmed, about 10 minutes.