Heat 1 tablespoon oil in the pot over medium heat. Add onion, garlic and a pinch of salt; cook, stirring occasionally, until the onion is starting to brown, 5 to 8 minutes. Stir in broth and the reserved cooking liquid, scraping up any browned bits. Stir in cabbage and ground pepper. Bring to a boil. Adjust heat to maintain a simmer, cover and cook until the cabbage is very tender, about 25 minutes. Season with the remaining 1/2 teaspoon salt.