Preheat a grill to high or an oven to 425°F (220°C).
Slice the chicken breasts so you have four pieces and pound each to an even 4-ounce thickness.
In a large bowl, combine the diced baby potatoes, sliced bell pepper, sliced onion, carrot matchsticks, minced garlic, olive oil, dried basil, oregano, parsley, garlic powder, onion powder, thyme, red pepper flakes (if using), salt, and pepper; toss to coat evenly.
Lay out four large sheets of aluminum foil. Divide the vegetable mixture evenly among the sheets, place one chicken piece on top of each portion, and add 1 tablespoon unsalted butter to each packet.
Seal each foil packet tightly to prevent steam from escaping.
Cook the packets until the chicken reaches 165°F (74°C) internal temperature: on the grill it will take about 15–25 minutes (around 20 minutes typical), or in the oven about 30–45 minutes (around 35 minutes typical).
Carefully open the packets to release steam. Drizzle with a little olive oil and finish with chopped parsley, a squeeze of lemon juice, and freshly grated Parmesan; adjust salt and pepper if needed.
Stovetop option: follow steps for prepping. In a large skillet, heat 2 tablespoons oil and cook chicken in a single layer 2–4 minutes per side, adding 1 tablespoon butter after flipping, until fully cooked; transfer and keep covered. Add more oil and 1 tablespoon butter to the skillet and cook the veggies until crisp-tender, then plate with the chicken and finish with Parmesan and lemon juice.
