Melt the butter in a saucepan over medium heat. Add the onion and cook for 4-5 minutes to soften. Add the swiss chard and cook for 5 minutes, stirring often until softened. Add the stock and beans and gently bring to a boil. Season with sea salt and black pepper.
Toast the ciabatta until golden on both sides. Rub the toasted bread with the cut sides of the garlic, then place each one in a serving bowl. Drizzle each piece of bread with olive oil and ladle soup over the bread. Sprinkle with parmesan cheese and serve immediately.