Preheat oven to 325 degrees.
Remove and reserve stems from chard leaves. Bring a large pot of salted water to a boil and prepare a large bowl of ice water. Blanch half of the chard leaves for 10 seconds and immediately transfer to the ice bath; let cool. Drain and squeeze out excess water. Roughly chop and transfer to a blender or food processor and purée until coarse. Add the broth (if using) or water, chiles, cilantro, cumin and ¼ cup olive oil; purée until thick and smooth. Finely chop the chard stems and roughly chop the rest of the leaves. Heat remaining 2 tablespoons oil in a large skillet over medium. Add onions and sauté until fragrant; then add the stems and continue to sauté until tender, about 5-8 minutes. Working in batches, add chard leaves and cook about 2 minutes or until leaves are wilted. Season with salt and pepper. Add the purée to the skillet and stir together. Using a spoon, create 5 small wells. Gently crack the eggs into the wells. Transfer the skillet to the oven and cook until the egg whites are fully set but the yolks are still a little bit jiggly, 20 to 25 minutes. Remove from oven and sprinkle with harissa or aleppo pepper and more cilantro leaves.