In a medium bowl, combine the ricotta, egg, salt, pepper and parsley. Stir until well combined, set aside.
Trim the ends of the squash. Using a mandolin (or with a sharp knife), slice lengthwise into thin strips. (I used a mandolin on the 1/16 of an inch setting). Lay slices a single layer on a kitchen hand towel and continue until all are sliced thin.
To assemble, slightly overlap two slices of the zucchini. Add one tablespoon of the ricotta mixture at on end then gently roll. Once rolled, nestle each zucchini roll-up seam side down into the simmering sauce. Continue until all are rolled and nestled. (You should end up with 12-14 roll-ups).
If you have any remaining ricotta mixture, scatter some dollops on top of the roll-ups in the skillet.
Transfer skillet to the preheated oven and cook, uncovered, until the zucchini is just tender, about 10 minutes. You want your zucchini to still have a slight bite to it, and not be soggy.
Remove from oven and allow to cool for 5 minutes. Garnish with fresh basil, serve and enjoy!