Heat the oven to 375°F and arrange a rack in the middle.
Bring a large pot of heavily salted water to a boil over high heat. Add the pasta shells, stir, and cook until al dente, about 10 minutes. Place a colander in the sink and drain the shells. Rinse with cold water until cool and then drain well. Transfer the shells to a medium bowl and set aside. Return the colander to the sink.
Heat the oil in a large frying pan over medium heat until shimmering. Add the onions, garlic, oregano, 1/2 teaspoon of the salt, and the measured pepper and cook, stirring often, until the onions have softened, about 5 minutes. Add the chard and cook, tossing constantly with tongs, until completely wilted and tender, about 5 minutes. Transfer the mixture to the colander and let sit, stirring occasionally, until cool enough to handle, about 10 minutes.
Meanwhile, place the ricotta, 1/4 cup of the Parmesan, the egg, and the remaining 1/2 teaspoon salt in a large bowl and stir to combine; set aside. Place the marinara or tomato sauce and water in a medium bowl and stir to combine; set aside.
When the chard mixture is ready, squeeze large handfuls to release any excess liquid and transfer to a cutting board. Finely chop and add to the ricotta mixture. Stir until evenly combined. Taste and season with salt and pepper as needed. Transfer the ricotta-chard mixture to a large resealable plastic bag and snip 1/2 inch off one bottom corner.
Evenly spread 1 cup of the tomato sauce mixture on the bottom of a 13-by-9-inch baking dish. Pipe about 2 tablespoons of the ricotta mixture into each pasta shell and place in a single layer, open side up, in the baking dish. (Alternatively, use a spoon to fill the shells.) Pour the remaining tomato sauce mixture evenly over the shells and sprinkle with the remaining 1/2 cup Parmesan.
Cover the dish with foil and bake until the sauce just starts to bubble around the edges, about 20 minutes. Remove the foil and continue baking until the sauce is bubbling vigorously and the edges of the pan have started to brown, about 10 minutes more. Remove from the oven and let cool 5 minutes before serving.