Preheat the oven to 400°F/200°C. Clean the mushroom and remove the stalk. Brush the top with olive oil and bake until cooked through and juicy - this will vary according to the size of the mushroom.
Heat 1 tablespoon of butter in a frying pan and toss in the leaks and bacon. Cook until the bacon is crispy then crack in the egg, splash of milk, cheese, salt, pepper and thyme.
Quickly and vigorously whisk so the egg forms a scramble, continue mixing until the egg is solid and cooked through - between 3 and 5 minutes.
When the mushroom is cooked, remove it from the oven and stuff with the scramble.