Prepare ingredients per instructions above. Preheat the oven broiler. Lightly toast the rolls on a baking sheet. Spread mayo inside the roll.
Heat half the olive oil in a skillet over medium heat. Sauté the onions and bell peppers until golden brown and caramelized, about 5 minutes. Transfer to a plate and set aside.
Add the remaining olive oil to the skillet. Add the shaved steak in an even layer and let it brown undisturbed for 2 minutes. Sauté until fully cooked through and season with salt and black pepper to taste. Ensure the steak reaches an internal temperature of 145°F (63°C) for medium-rare or 160°F (71°C) for medium, for safe consumption.
Divide the steak into two portions in the skillet. Top each portion with 2 slices of American cheese. Turn off the heat and let the cheese melt. Cover with a lid for faster melting, if desired. Place each portion of steak and melted cheese into a roll.
Add the lemon to the sparkling water. Serve over ice, if desired.
Plate the cheesesteaks with carrot sticks and ranch dressing on the side. Enjoy with refreshing lemon sparkling water.