Prepare the lobster. You may do so the day before.Preheat the oven to 400ºF.
Arrange the cast iron dishes on a baking tray and spread a little duck fat in each. Divide the diced potatoes evenly among the dishes and add a sprig of fresh thyme and a pinch of salt and pepper. Bake for 15 minutes, but don't allow to brown.
Whisk together the eggs and seasoning and set aside. You may add a little cream to the eggs, but I prefer it without for this particular dish. Chop your leek and onions. Chop up the lobster. Set aside.
Remove the tray with potatoes from the oven after 15 minutes and evenly distribute the leek and onions among the dishes. Combine with the potatoes and return to the oven for 10 minutes.
Remove from the oven and evenly distribute the lobster pieces among the dishes and combine with the potato mixture. Pour the whisked eggs over each and return to the oven for 5-7 minutes.
Remove from oven, top with cheese, lobster, parsley and tomato. Serve with a side of arugula salad. Enjoy!