Make the hollandaise sauce: pour 2 of the eggs in a saucepan in a bain-marie, start stirring with a whisk and add the lemon juice and salt. Add the EVO oil little by little, always stirring. Cook for about 5 minutes, until the sauce, becomes light-colored. Remove it from the heat and keep it aside, covering it with contact film.
Grill the Prosciutto Toscano DOP and toast the muffins. Prepare the poached eggs: bring the water to a boil in a large pot and add the vinegar. Open the eggs in a small bowl and slide them into the water. Let it cook for 2-3 minutes until the clears have a firm consistency. Remove the eggs with a slotted spoon and drain well.
Place the grilled Prosciutto Toscano DOP on the muffin, add the egg on top and garnish with the hollandaise sauce.