Wash the tomatoes and cut off a lid. Remove the seeds with a teaspoon and cut out the pulp. Put the tomato lids and the pulp in a tall bowl, puree with the hand blender and set aside.
Salt and pepper the inside of the hollowed out tomatoes and sprinkle with oregano. Cut the ham without a fat rim into narrow strips and fill them with the tomato.
Preheat the oven to 180 ° C.
Slip a beaten egg into each tomato, lightly salt and sprinkle with parmesan. Put 1 teaspoon of butter on each. Place the tomatoes on a baking tray or in a baking dish. Place on the middle rack of the oven and let the eggs set for 12-15 minutes.
In the meantime, season the pureed tomato flesh with olive oil and red wine vinegar, salt and pepper and serve with the stuffed tomatoes.