Preheat the oven to 425°F (220°C). A hot oven helps the chicken skin crisp and the veggies caramelize.
Prep the pan. Line a large rimmed sheet pan with parchment paper or foil for easier cleanup. Lightly oil the surface.
Mix the seasoning. In a small bowl, combine smoked paprika, oregano, thyme, black pepper, salt, and minced garlic. Stir in 2 tablespoons olive oil and the lemon juice to form a paste.
Season the chicken. Pat the chicken dry with paper towels.
Rub about half the seasoning paste under the skin (if using skin-on) and over the surface. Place the chicken on the pan, skin side up.
Prep the veggies. In a large bowl, toss broccoli, carrots, bell pepper, red onion, and potatoes with the remaining 1 tablespoon oil and remaining seasoning paste. If it looks dry, add another splash of oil.
Arrange on the pan. Spread the vegetables around the chicken in an even layer.
Leave a little space between pieces for better browning.
Bake for 35–45 minutes. If using bone-in thighs, start checking at 35 minutes. Boneless pieces may be done in 20–30 minutes. The chicken is done when it reaches 165°F (74°C) in the thickest part.
Potatoes should be fork-tender.
Optional broil. For extra color, broil for 2–3 minutes at the end. Watch closely to avoid burning.
Finish and serve. Squeeze fresh lemon over the top and sprinkle parsley. Taste and add a pinch of salt if needed.