Arrange a rack in center of oven; preheat to 450°. Cut each cheese stick into 5 pieces.
On a lightly floured surface, divide dough in half. Roll each piece to an 18" x 4" rectangle. Cut into 2" squares (you’ll need 33). Wrap each square around a piece of mozzarella and form a tightly sealed ball.
Arrange balls, seam side down and touching, on a parchment-lined baking sheet in a Christmas-tree pattern.
In a small bowl, beat egg with 1 Tbsp. water. Brush egg wash on dough balls.
Bake tree until golden, 15 to 20 minutes.
In a small bowl, whisk butter, Parmesan, parsley, rosemary, and basil; brush on tree. Sprinkle with Parmesan, parsley, and red pepper flakes. Serve with marinara alongside.
