Preheat oven to 375°F (190°C). Lightly grease a 9-inch pie plate.
Heat olive oil in a large skillet over medium heat. Add the chopped onion and cook until softened, about 5 minutes. Add the minced garlic and cook for 1 minute more until fragrant.
Add the shredded zucchini, 1/2 teaspoon salt, and 1/4 teaspoon pepper to the skillet. Cook, stirring occasionally, until the zucchini has released its liquid and it has mostly evaporated, about 5-7 minutes.
Remove the skillet from heat. Stir in the fresh parsley and basil.
In a medium bowl, whisk together the lightly beaten eggs, mozzarella cheese, and Parmesan cheese.
Add the cooked zucchini mixture to the egg and cheese mixture and stir to combine. Season with additional salt and pepper to taste.
Unroll one can of crescent rolls and press the seams together to form a solid circle. Press the dough into the prepared pie plate, covering the bottom and up the sides.
Pour the zucchini filling evenly over the crescent roll crust.
Unroll the second can of crescent rolls and cut them into strips. Arrange the strips over the top of the filling in a lattice pattern or sprinkle them around the edges.
Bake for 30-35 minutes, or until the crust is golden brown and the filling is set.
Let the pie cool for 5-10 minutes before slicing and serving.