Heat the oil in a large, low-sided stockpot or Dutch oven set over medium-high heat. Add the onions and cook until they start to soften and are brown in parts, about 5 minutes. Add the garlic and ham, and cook until the garlic softens, about 2 minutes. Add the collard greens, broth, vinegar, 1 teaspoon salt and 1/4 teaspoon pepper. Stir to combine and cook, covered, until the collards are tender, 20 to 30 minutes. Stir in the black-eyed peas and butter, and cook until the beans are warmed through, about 5 minutes.
Meanwhile, fill a large saucepan three-quarters with water. Salt lightly and bring to a boil. Add the oats and cook, stirring occasionally, until just tender, about 15 minutes. Drain the oats and divide them among six bowls. Top with the collard greens, ham and black-eyed peas. Serve immediately with hot sauce if using.
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