Place an oven rack in the center of the oven. Preheat the oven to 400 degrees F. Butter a 9 by 13-inch glass baking dish. Set aside.
Remove the thick stem from the center of each chard leaf. Cut each leaf in half lengthwise. Trim the ends from the leaves to make each leaf-half about 7 inches long and 5 inches wide. Bring a large pot of salted water to a boil over high heat. Add the chard leaves and cook for 10 seconds. Remove the leaves and rinse with cold water. Drain on paper towels and set aside.
For the filling: In a medium bowl, mix together the brown rice, arugula, goat cheese, lentils, mint, olive oil, 1 teaspoon salt, 1/2 teaspoon pepper and garlic. Season with additional salt and pepper.
Spoon 1/3 cup of the filling onto the end of each chard leaf and roll up like a jellyroll.
Spoon 1 cup marinara sauce on the bottom of the prepared pan. Arrange the rolls, seam-side down, in a single layer on top of the sauce. Spoon the remaining sauce on top and sprinkle with the Parmesan. Drizzle with olive oil or dot the top with butter, if using, and bake until the cheese begins to brown and the rolls are heated through, about 25 minutes. Cool for 5 minutes and serve.