Discard dandelion green roots; wash greens well in salted water.
Cut leaves into 2-inch pieces. Cook greens uncovered in small amount of salted water until tender, about 10 minutes. Sauté onion, garlic, and jalapeño pepper in oil. Drain greens; add to onion garlic mixture.
Taste dandelion greens and season with salt and pepper. Serve dandelion greens with grated Parmesan cheese and scrambled eggs.