Wash the courgettes and gently remove the cap.
With the help of a digger or a teaspoon, remove the pulp, cut it into cubes and brown it in a pan with a drizzle of oil and the chopped shallots for about 7-8 minutes. If necessary, add half a glass of water. Season with salt and pepper.
Steam the courgette cups emptied of the pulp for 15 minutes (if you have used the steam oven), fill them with the cooked pulp and shallot, add an egg yolk to each courgette and bake at 180° C for a ten minutes (the egg yolk must remain soft).
While the courgettes are in the oven, cook the egg whites in a pan, seasoning them with a pinch of salt and pepper and a few thyme leaves.
When the courgettes are cooked, add the cooked egg white over the yolk and finish with a sprinkling of Parmesan cheese and a few leaves of fresh thyme.