Heat the butter and olive oil in a large Dutch oven over medium-high heat. Add the garlic, onion and jalapeno and cook, stirring, until softened, 3 to 4 minutes. Add the stock, ham, salt, pepper, collards and beans. Bring to a boil and reduce to a simmer. Cook until the collards have softened and the flavors have come together, about 20 minutes.
Stir in the vinegar and taste. Adjust the seasonings as needed. Serve in bowls and garnish with the Parmesan and parsley. Serve each bowl with a chunk of crusty baguette.