Bring a large pot of salted water to a boil over high heat. Add dandelion greens and cook until wilted, about 3 minutes. Using a slotted spoon or a wire skimmer, transfer greens to a colander to drain. Add rapini to boiling water and cook until soft, 3 to 5 minutes. Using a slotted spoon or a wire skimmer, transfer rapini to a colander to drain. Add cabbage to boiling water and cook until wilted, about 3 minutes. Drain and set greens aside.
In a large, heavy-bottomed pot, heat olive oil over medium heat. Add celery, garlic, bay leaf, and red pepper flakes. Cook, stirring occasionally, until celery and garlic are soft and translucent, about 3 minutes. Add pancetta and cook, stirring occasionally until lightly browned and crisp, about 3 minutes. Stir in greens and both brodos. Let simmer until greens are tender, about 10 minutes; season with salt and pepper. Add meatballs during the last 5 minutes of cooking, if desired.
Ladle soup into warmed bowls; drizzle with olive oil and serve immediately.
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