Preheat oven to 375 degrees Fahrenheit, and lightly grease a 13x18-inch baking sheet.
Lay 4 boneless skinless chicken breast out onto the baking sheet evenly spaced apart. Zest 1 medium lemon and set the zest aside. Then drizzle the juice from the lemon over the chicken breasts. Season with 1/2 teaspoon salt and 1 teaspoon lemon pepper.
In a large mixing bowl, combine your quartered potatoes and 2 cups broccoli florets. Melt 3 tablespoons butter and pour it over the vegetables along with 3 tablespoons olive oil, 5 teaspoons minced garlic, 1/2 cup freshly grated Parmesan cheese, 1/2 teaspoon salt, and 11/4 teaspoon black pepper. Toss until evenly coated.
Spread potatoes and broccoli out into an even layer on the sheet pan, surrounding the chicken.
Bake in the preheated oven for 35 to 40 minutes, until chicken reaches an internal temperature of 165℉ and the potatoes and broccoli are fork tender.
Remove the pan from the oven. Garnish with lemon zest and 1 teaspoon chopped fresh parsley (optional).
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Notes
You can also sprinkle up to 1 tablespoon of grated Parmesan cheese onto each of the chicken breasts if you want more cheesy goodness. Place the pan under a broiler for 2 to 3 minutes, just until the cheese is slightly browned.