Preheat the oven to 425° F.
Line a sheet pan (or two, if needed) with parchment paper or Silpats, or rub lightly with olive oil. Trim the stem end of each zucchini. Stand each vertically,and make 1/4-inch thick cuts down to create long slices—they don't have to be perfect. Or lie the zucchini flat on the cutting board and carefully slice along the length keeping the knife parallel to the surface as you go.
Arrange the slices on the prepared sheet pan(s) and drizzle the zucchini lightly with olive oil. Season with salt and pepper. Transfer the pan(s) to the oven and roast for 10 to 15 minutes, just until the zucchini is pliable enough to be rolled into a coil. Remove pan(s) from the oven.
Meanwhile,in a large sauté pan set over high heat, heat the tablespoon of olive oil until shimmering. Add the chopped chard leaves, season with a pinch of salt and pepper, and sauté, rearranging with tongs as necessary. Cook the chard for about 2 minutes or until wilted. Remove pan from heat.
To make the filling, in a medium bowl, stir together the ricotta, lemon zest,thyme, and 1/4 teaspoon salt. When chard has cooled briefly, stir it into the ricotta mixture. Taste mixture. Add more salt to taste—this is your chance to make sure the filling is seasoned properly.
Spoon tomato sauce into two 9-inch round baking dishes or one 9×13-inch baking dish—the bottom of the dish should be covered in a thin layer. Place a spoonful (about 2 teaspoons) of filling at one end of each of the zucchini slices. Roll the slice into a tight coil and place it seam-side down in the dish on top of the tomato sauce. Drizzle lightly with olive oil. Season lightly with salt and pepper. Transfer to the oven and bake until the sauce has reduced slightly and is bubbling, and the rolls are lightly golden on top,about 25 minutes. If the rolls are still not golden after the 25 minutes, remove the pan from the oven and preheat the broiler. Broil the involtini for about 3 minutes keeping a close watch the entire time. Remove pan from the oven and sprinkle finely grated Parmesan over the top.