1) Preheat oven to 350 degrees F.
2) In a small bowl, stir together salad mix ingredients and set aside. It’s actually best if these can be at room temp so it’s fine to leave them out while you make the other sandwich stuff.
3) Slice the rolls in half and hollow out most of the filling. In the bottom half of the rolls, sprinkle some cheese. Toast rolls for 2-3 minutes until cheese starts to melt.
4) Lightly saute diced ham in a tablespoon of olive oil over medium-high heat until the ham starts to brown (optional). Then add ham to the cheese half of the roll. You don’t have to cook the ham first, but I like how it gets a bit crispy.
5) In a large skillet over medium heat, melt butter and coat the pan. Add eggs and scramble until they are just cooked through. Try not to overcook them. Season eggs with salt and pepper and split them into four even stacks (1 for each sandwich). Stack eggs on ham. Return rolls to oven for 2-3 minutes.
6) Stuff the top part of the roll with the salad mix.
Press the sandwiches together and eat while warm! Cut them in half to make them a little easier to eat!