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1
In a Dutch oven or heavy 5-quart pot, combine beets, beans, and enough water to cover; season with salt and pepper.
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2
Bring to a boil; reduce to a simmer, and cook (uncovered) until beets are tender when pierced with the tip of a sharp knife, 45 minutes to 1 hour (add more water to cover, as needed).
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3
Transfer beets to a bowl; when cool enough to handle, rub off skins with paper towels, then cut into dice.
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4
Continue to cook beans until tender, about 1 hour more; pour off any excess liquid.
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5
On a cutting board, finely chop garlic, and sprinkle with salt.
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6
Using a chefs knife, press flat side of blade back and forth across garlic to make a paste.
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7
In a small skillet, heat oil over medium; add garlic paste, scallion, and cilantro.
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8
Cook, stirring frequently, until scallion has softened, 2 to 4 minutes.
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9
Stir scallion mixture into beans; cook over medium heat to allow flavors to meld, about 5 minutes.
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10
Serve beans and beets over rice, with lime wedges alongside; garnish each portion with cheese, chopped scallion, and a sprig of cilantro.
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11
The dish can be prepared through step 4 up to 3 days ahead; let cool completely before refrigerating in an airtight container.
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12
Reheat over medium before serving.