Preheat your oven to 400°F (200°C). Dice potatoes into bite-sized pieces and chop bell peppers and onion.
In a large mixing bowl, combine diced potatoes, bell peppers, and onions. Drizzle with olive oil, season with salt and pepper, then toss to coat evenly.
Pat chicken breasts dry with paper towels. Sprinkle ranch seasoning mix over both sides of each breast.
Spread tossed vegetables evenly across the bottom of the baking dish. Nestle seasoned chicken breasts on top, spacing them out evenly.
Bake in the preheated oven for 30-35 minutes until potatoes are fork-tender and chicken is cooked through (165°F / 74°C). Tent with foil if chicken finishes early.
Sprinkle shredded cheddar cheese evenly over the top. Switch oven to broil and broil for 2-4 minutes until cheese melts and bubbles with a golden brown finish.
Remove from oven, sprinkle fresh parsley over the top, and serve immediately.