Preheat oven to 325 degrees Fahrenheit (160 degrees Celsius).

Slice zucchini lengthwise into 1/4-inch (1/2-centimeter) thick slices. (I used a mandoline to get perfectly even slices.) Select the 15 longest slices and place onto two baking sheets in a single layer. Roast for 15 minutes, just until soft enough to roll, switching the pans midway through baking. Remove from oven and allow to cool.

While the zucchini is roasting, prepare the filling by placing the ricotta cheese, spinach, two cups mozzarella cheese, 1/2 cup Parmesan cheese, beaten egg, parsley, scallions, and salt in a medium bowl. Mix well to combine.

Working on a flat surface, spread a spoonful of filling over the length of each zucchini slice and roll up gently. Divide the filling evenly over all 15 slices.

Sauté the onion in butter in a medium saucepan until soft and golden, about 10–15 minutes.

Add garlic and stir for an additional two to three minutes until fragrant. Add mushrooms and cook an additional 10 minutes, or until softened. Add the flour and mix until well incorporated. Mixture will be thick and sticky.

Slowly add 1/2 cup milk at a time, stirring until no lumps remain. Add seasonings and cook just until heated through and slightly thickened.

Raise oven temperature to 350 degrees Fahrenheit (175 degrees Celsius).

Pour a third of the mushroom sauce into the bottom of a nine- by 13-inch  (20- by 30-centimeter) pan.

Place the zucchini rollups seam side down on top of the sauce. Pour the rest of the sauce over the top of the zucchini and sprinkle with the remaining 1/2 cup of mozzarella and 1/4 cup Parmesan cheese.

Bake uncovered for 35–40 minutes or until bubbly and the zucchini is tender. Broil for an additional two to three minutes until golden. Remove from oven and allow to rest for five to 10 minutes before serving.