Place dough on a piece of parchment or a silicone baking mat. Roll dough out to thin it, and press seams together. Cut dough in half down the center. Spread half of dough with a layer of pesto, stopping just short of the edges. Top with Parmesan and cover with prosciutto. Place remaining piece of dough on top and press down edges forming a big rectangle.
Cut off corners at the top of rectangle to establish the tree shape. With a sharp knife, make 1 inch diagonal cuts on each side, leaving 1 inch uncut in between “limbs.” Gently lift each limb and twist several times and pinch ends together. Make slits down the uncut tree trunk with the tip of a sharp knife. Brush pastry with beaten egg. Cover and refrigerate at this point until baking.
Bake pastry at 400 for 15-20 minutes or until puffed and golden. Carefully transfer to platter or serving board. Let guests pinch off a piece to eat.
Notes
For a bigger tree, use 2 sheets of puff pastry and double the filling ingredientsSweet & Savory Variation: spread pastry with fig jam and top with bleu cheese crumblesSweet Variation: spread with almond paste, or raspberry jam and chocolate or white chocolate chips