Season the shaved steak with salt and pepper.

Heat the olive oil in a pan over medium heat. Add the sliced onions and sauté until softened and beginning to brown. Add the shaved steak and brown well. Set aside.

Add the beef broth and rosemary to a pot. Bring the mixture to a simmer and cook for 15–20 minutes to allow the flavors to develop. Stir in the butter and taste. Adjust the salt and pepper if desired.

Preheat the oven broiler to low. Slice the rolls open and place them on a baking sheet. Toast under the broiler until golden brown, watching closely to prevent burning.

Using tongs or a slotted spoon, dip the beef into the au jus then portion onto the toasted rolls.

Optional: top with cheese and melt under the oven broiler.

Serve with the reserved au jus on the side for dipping.

In a pitcher, mix together the lemon juice, water, and sugar. Stir until the sugar dissolves completely. Serve over ice if desired.

Serve the French dip sandwiches with carrots and hummus, pickle spears, and glasses of homemade lemonade.