Prepare all ingredients as listed above.
Preheat the oven broiler.
Lightly toast the sub rolls on a baking sheet.
Heat half of 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 chicken and sauté until cooked through to an internal temperature of 165°F (74°C). Season with salt and black pepper to taste.
Divide the chicken into portions in the skillet. Top each portion with cheese and melt under the oven broiler.
Place each portion of chicken into a sub roll. Top with peppers and onions. Drizzle with ranch dressing or serve ranch on the side for dipping. Cut in half if preferred.
Add lemon slices to the sparkling water. Serve over ice if desired.
Serve the sandwich with carrot sticks, hummus, and lemon sparkling water.