In a large Dutch oven over medium heat melt the butter with the olive oil. Add the shallots and cook until caramelized, about 15 minutes (make sure the heat is rather low, if the heat is too high and your shallots will burn before they caramelize, patience is key).

Add the beans, broth, beer and ham bone to the pot, bring to a low simmer.

Allow to simmer until the beans are cooked through, about 2 hours.

Add the ham, salt and pepper, simmer for about ten minutes.

Ladle into bowls, top with parmesan and arugula before serving.