Preheat oven to 350ºF. Lightly coat or spray a medium baking dish with oil.
Heat the olive oil in a large skillet over medium-high heat. Add the garlic and mushrooms and cook for about 5 minutes, or until the mushrooms have released their juices and the liquid has evaporated. Add the chopped chard and heat until wilted, 1-2 minutes more. Remove from heat, drain off any liquid (this is important!), and season to taste with salt and pepper.
Transfer the mushrooms and greens to a large bowl. Stir in the ricotta, Parmesan, and Italian seasoning. Taste the filling and add more salt and pepper if needed, then stir in the egg.
Spread 3/4 cup of marinara sauce on the bottom of the baking dish. Fill the cooked shells with the ricotta-vegetable mixture and place them in the baking dish. When all the shells are stuffed, spoon the remaining marinara sauce over the top, then sprinkle evenly with the mozzarella cheese.
Cover the baking dish with foil and bake for 30 minutes; remove the foil and bake for 15 minutes more, or until the mozzarella has melted and the sauce is bubbling. Let the shells cool for 5 minutes, then serve.