Cut an X into one side of each tomato. Bring a large pot of water to a boil. Add tomatoes and cook for 1 minute. Drain in a colander, and carefully peel and slice tomatoes.

Melt butter in a large skillet over medium heat and cook onions until soft and translucent, about 5 minutes. Add tomato slices and season with salt. Cook until tomatoes are soft and most of the liquid has evaporated, about 10 minutes.

Beat eggs and milk in a small bowl. Season with salt and stir in parsley. Pour egg mixture on top of tomatoes in the skillet. Cook over low heat until eggs have set, 5 to 10 minutes. Serve immediately.