Combine vegetable broth, wild rice, brown rice, and olive oil in a saucepan; bring to a boil, reduce heat to low, cover with a lid, and simmer for 20 minutes. Stir balsamic vinegar, sherry, garlic, salt, black pepper, and cardamom into rice; cover with a lid and continue simmering until flavors start to combine, about 10 minutes.

Stir black beans, mushrooms, cranberries, and parsley into rice mixture; continue cooking over low heat until rice is tender and mixture is hot throughout, 10 to 15 minutes more.