Prep the ingredients per instructions above.

Boil the eggs: Place the eggs in a small saucepan and cover them with water. Bring the water to a boil, then reduce the heat to a gentle simmer. Cook the eggs for 9-12 minutes. Transfer the eggs to a bowl of ice water to cool for a few minutes. Gently crack and peel the hard-boiled eggs. Set aside.

Season the beef with salt and pepper.

Heat the oil in a pot on medium heat. Saute the onions until softened and starting to brown. Then stir in the broth, beef, and rosemary. Bring to a low simmer until the flavor concentrates, about 15 to 20 minutes. Then add in the butter. Taste and season with salt and pepper to taste.

Finish the deviled eggs: Slice the eggs in half lengthwise. Carefully remove the yolks and place them in a mixing bowl. Add mayonnaise, Dijon mustard, white vinegar, salt, and pepper to the yolks. Mix well until the filling is smooth and creamy. Adjust the seasoning to your taste. Using a spoon or a piping bag, fill each egg white half with the yolk mixture.

Mix together the ingredients for the homemade lemonade. Serve over ice if desired.

Preheat the oven broiler on low. Slice open the rolls and place them on a baking sheet. Toast the bread under the broiler until golden brown (keep a close eye on the bread so that it doesn't burn).

Using tongs or a slotted spoon, place the beef on the roll.