Heat oil in a Dutch oven over medium heat. Add onion; cook 5 minutes, stirring occasionally. Add mushrooms; cook 3 minutes, stirring occasionally. Stir in grano and white wine; cook until liquid is almost evaporated (about 2 minutes), stirring often. Stir in broth. Cover, reduce heat, and simmer 25 minutes.
Add kale, salt, and garlic; cook 6 minutes or until kale is tender, stirring often. Add parsley and remaining ingredients.