Preheat the oven to 400F. Spread ¼ cup marinara sauce on the bottom of a 13 x 9-inch baking dish.
Cut the zucchini lengthwise, into ¼-inch thick slices until you have a total of 12 slices about the same size.
Season both sides of the zucchini with ½ tsp salt and pepper, then grill on a grill pan over high heat until pliable and grill marks form, about 2 minutes on each side.
In a medium bowl, beat the egg then mix together with ricotta, Pecorino Romano, basil, garlic, ⅛ tsp salt and ⅛ tsp pepper.
Spread the ricotta mixture (about 1 ½ tablespoons each) evenly onto each zucchini slice.
Roll up slices and arrange them each seam side down in the prepared dish.
Top each with 1 tbsp marinara sauce and 1 tbsp mozzarella cheese and tightly cover with foil.
Bake 20 minutes, or until the cheese is hot and melted.