Heat oil in a Dutch oven over medium heat
Arrange garlic halves, cut side down, in pot and scatter onion around; season with salt and pepper. Cook, stirring onion occasionally but keeping garlic cut side down, until the onion is deep golden, about 20 minutes
Add kale to the pot by the handful, stirring and letting it wilt before adding more. Season with salt. Cook, stirring often, until all the kale is deep green and wilted, about 3 minutes. Add 1.5 cups of water, cover pot partially with a lid, and cook until liquid is reduced by half and kale is tender, about 12-15 minutes
Add Parmesan to braised kale and cook, stirring, until cheese is melted and incorporated - sauce will thicken slightly - about 5 minutes. Taste and season with more salt and pepper as needed