1. Bring a large pot of water to a boil. Add the dandelion greens and blanch for 1 to 2 minutes. Drain the greens thoroughly, patting them as dry as possible with paper towels.
2. Melt the butter in a 10-inch saute pan over medium heat. Saute the leeks in the butter until tender, about 5 minutes. Add the dandelion greens 1 handful at a time. Cook each handful until wilted, then add more.
3. When all the greens are wilted, crack the eggs into the pan on top of the greens. Top with feta cheese and cook uncovered until the whites of the eggs are set, about 5 minutes.