Heat oil in a sauté pan over medium heat and add cippolini and garlic; cook until tender.
Add mushrooms and cook for 5 minutes. Add heavy cream and cook for 2 minutes. Remove from heat and stir in the crème fraiche, dandelion greens and chives. Add salt and pepper to taste.
Heat pasta briefly in boiling water; drain and reserve.
To assemble, place one pasta sheet in center of plate and spoon mushroom mixture over; cover with second pasta sheet and spoon mushroom mixture over; cover with third pasta sheet. Spoon the fava bean coulis over and around lasagna, along with any excess mushrooms.