Heat oil in a large frying pan over medium heat. Add sausage and brown, breaking up with the back of the spoon while cooking. Add garlic and cook a minute more. Add beans and stock and scrape up any browned bits that are stuck to the bottom of the pan. Bring to a boil, then reduce heat to a simmer and cover. Cook until beans are just tender, about 3 minutes.

Meanwhile, bring a large pot of heavily salted water to a boil. Add pasta and cook according to package instructions. Drain, reserving 1 cup of pasta water, and return pasta to the pot.

When beans are barely tender, add chard and cook until wilted. Season with salt and pepper and pour sausage mixture over pasta, add parsley and more pasta water if it seems dry. Toss together to combine and serve, drizzling each bowl with a little olive oil and a sprinkling of Parmesan cheese if desired.