If using beets, preheat oven to 400°F. Cut greens from beets, leaving about 1 inch of stem attached; reserve about 8 cups greens, lightly packed. Wash and dry the beets. Wrap in foil and roast until tender, 1 1/4 to 1 1/2 hours, depending on the size. (Alternatively, place beets in a microwave-safe dish, add 1/4 cup water, cover and microwave on high for 20 to 25 minutes.) When the beets are cool enough to handle, peel 4 of them and cut into 1/2-inch wedges. You should have about 2 cups. Place in a medium bowl. (Reserve the remaining beets for another use.)
Using a mortar and pestle or the side of a chef's knife, mash garlic and salt into a paste. Transfer to a large bowl. Add vinegar and whisk to blend. Add oil, oregano and pepper, whisking until blended. Measure out 1 tablespoon and add to the beet wedges; toss to coat. Add beans to the remaining dressing and toss to coat. Let marinate at room temperature until ready to use.
Place onion in a small bowl, cover with cold water and add a handful of ice cubes; let stand for 10 minutes, or until ready to use.
Meanwhile, bring 2 cups lightly salted water to a boil in a large wide pan. Wash beet greens in several changes of water; trim the stems. Add the greens to boiling water, cover and cook until tender, about 5 minutes. Drain well, pressing on the greens with the back of a spoon to remove excess moisture. Cut into 1-inch pieces.
Drain the onion. Add to the beans along with greens; toss to coat. Spoon the salad onto a serving platter or individual plates and garnish with the beets, if using. Serve immediately.
Soaking the onion in ice water for 10 minutes or more renders it less pungent and more crisp.
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