Garlic and Parmesan Braised Greens

Name: Garlic-and-Parmesan-Braised Greens
Ingredients: ⅓ cup extra-virgin olive oil, plus more for serving; 1 head of garlic, halved crosswise; 1 large onion, thinly sliced; Kosher salt, freshly ground pepper; 2 bunches Tuscan kale or collard greens, ribs and stems removed, leaves torn; 2 oz. Parmesan, finely grated