In a medium saucepan, cook the beets in 1 quart boiling water until just tender, about 15 to 20 minutes. Drain; allow to cool, then peel and dice. Set aside.
Rinse the saucepan and bring a second quart of water to a boil over high heat. Add the broccoli spears and cook until tender and bright green, about 3 minutes. Drain and place in a bowl of ice water to chill. When chilled, drain and set aside.
In a large bowl, combine the beets, broccoli, dandeloin greens, green onions, garlic, parsley, cilantro and, if desired, the peanuts.
In a small bowl, whisk together the olive oil, vinegars, honey, and salt and pepper. Pour this vinaigrette over the vegetables and gently toss to lightly coat all ingredients. Serve immediately.