Hearty autumn greens take on new life when braised in a miso butter–laced broth. These richly flavored greens make a versatile side dish for everything from turkey and fish to sweet potatoes and squash.
Heat butter and oil in a large pot over medium until butter is melted. Add miso; cook, stirring often, until miso begins to bubble, about 2 minutes. Add garlic and ginger; cook, stirring occasionally, until garlic and miso are lightly browned and ginger softens, 4 to 5 minutes. Remove garlic from pot; set aside.
Add broth to pot; bring to a boil over high. Stir in kale and collards in large handfuls, letting each handful wilt slightly before adding more. Cover and reduce heat to low; simmer until greens are tender but not mushy, 18 to 24 minutes. Stir in vinegar and salt. Using tongs, transfer greens to a shallow serving dish; discard ginger. Ladle broth over greens. Sprinkle with crispy garlic, and serve.
Greens can be cooked up to 3 days ahead and stored in an airtight container in refrigerator.