I have been eating these since I was a kid, except without the parsley. Love it on toasted bread and you could use Miracle Whip or butter. You could even add some radish slices, sliced cheese, lettuce, cooked bacon, ham or scrambled eggs. Yummy.
I used to eat these all the time as a kid...great with a cheese slice,ketchup, and mustard! (It's almost like a burger without the burger).
We used to have these sandwiches when the tomatoes in my Aunt and Uncles garden were ripe and we had fresh baked rye bread from the bakery....great memories! I used green onions, omitted the parsley, and also used a good amount of salt and pepper. If you can get really fresh tomatoes they are the best for this sandwich.
Very surprised to find that this was an actual feature on a cooking show. I make this often when the sweet onions and good tomatoes are in season. I also like this with butter rather than mayo sometimes. The only thing I don't do is the parsley edges and I too cram the tomatoes in the sandwich. I love this on all types of bread too, try the rye, pumpernickle swirl bread with this. Its really yummy.