Heat the oil in a large heavy saucepan or Dutch oven over med-high heat. Add the sausage and saute until brown, 8-10 min. Add the swiss chard and garlic & saute until the chard is wilted and the garlic is fragrant, about 3 minutes. Add the tomatoes, broth, basil & mint. Reduce heat & simmer while you cook the pasta.
Bring a large pot of salted water to a boil. Add the pasta and cook until al dente; drain well. Transfer to warm serving bowl.
Season the pasta sauce with salt & pepper. Add the sauce to the pasta and toss well. Serve immediately; sprinkle with Parmesan if desired.