Preheat oven to 425 degrees F. Line a large baking sheet with parchment paper or spray with nonstick cooking spray; set aside.
Place cut potatoes and broccoli in a large mixing bowl or resealable gallon-sized bag. Drizzle oil over vegetables and toss to coat. Sprinkle ranch dressing mix and parmesan cheese over vegetables and stir or shake to coat again.
Spread vegetables in an even layer on prepared pan and bake for 25-28 minutes or until potatoes are golden brown and broccoli is tender.