Heat a medium Dutch oven over medium heat. Add 1/4 cup of the oil to the pan along with the garlic and onions. Season with 1/2 teaspoon salt. Cook the onions slowly, stirring often with a wooden spoon, until they are soft and tender, about 8 minutes. Add the cabbage and an additional 1/2 teaspoon salt and stir to combine. Cook until the cabbage wilts, about 2 minutes. Stir in the potatoes and enough broth to cover the mixture. Season with 1 teaspoon salt. Bring the mixture to a simmer and cook, stirring often, until the liquid is reduced by half, the potatoes are tender and the cabbage is silky and soft, 30 to 35 minutes. Using a potato masher or a whisk, crush the mixture until it loosely resembles the consistency of mashed potatoes. Stir in the remaining 1/4 cup oil and serve sprinkled with chives.