Preheat and prep: Heat the oven to 425°F (220°C). If using a stovetop skillet, choose a large oven-safe one.
Pat the chicken dry and cut large breasts in half horizontally for even cooking.
Season the chicken: Mix 1 teaspoon salt, 1/2 teaspoon black pepper, 1 teaspoon smoked paprika, and 1 teaspoon Italian seasoning. Rub over the chicken with 1 tablespoon olive oil.
Toss the veggies: On a sheet pan (or in a bowl), toss broccoli, bell pepper, onion, tomatoes, and carrots with 1 tablespoon olive oil, a pinch of salt and pepper, and a little paprika. Spread in a single layer, leaving space for the chicken.
Sear for flavor (optional but great): Heat 1 tablespoon butter in the skillet over medium-high.
Sear the chicken 2–3 minutes per side until lightly browned. Transfer to a plate. If you’re using only a sheet pan, skip this step and go straight to roasting.
Make the garlic butter: Lower the heat to medium.
Add 2 tablespoons butter and the minced garlic. Stir for 30–60 seconds until fragrant. Add lemon zest and juice, plus the broth if using.
Simmer 1 minute. Taste and adjust salt.
Combine and roast: Arrange the chicken among the veggies on the sheet pan (or nestle into the skillet). Spoon the garlic butter over everything.
Roast 15–20 minutes, until the chicken hits 165°F (74°C) and veggies are tender with browned edges.
Finish: Dot with the remaining 1 tablespoon butter if you like extra gloss. Sprinkle chopped parsley or thyme and a pinch of red pepper flakes. Add a small shower of Parmesan if you want a savory boost.
Serve: Spoon the pan juices over the chicken.
Serve as-is, or with rice, crusty bread, or mashed potatoes to soak up the sauce.