Preheat the oven to 350 degrees.
Fill a large pot with salted water and bring to a boil and cook pasta according to package directions, reducing the time by a minute or two since the pasta will continue cooking while it bakes in the oven.
Heat a large cast iron or oven safe pan over medium heat. Add the olive oil and swiss chard stems and sauté for 2 minutes, then add the leaves and sauté until wilted, about 3 minutes. Season with salt (about ¼ tsp)
Meanwhile, make the tomato sauce (if making home-made)
In the skillet that you sautéed the chard in, mix the cooked pasta, chard, cheeses and tomato sauce. Taste and add salt if necessary.
Sprinkle extra shredded mozzarella and parmesan cheese on top (if you like). Bake for 15 minutes. Broil for the last 1-2 minutes if you would like the cheese topping more brown and bubbling.
Remove from the oven and let cool for 5 minutes. Sprinkle with fresh chopped basil.