Preheat the oven to 375°F (190°C).
Spatchcock the chicken: remove the backbone, crack the breast bone, and flatten the chicken. Tuck in thhewings and season both sides generously with kosher salt and pepper.
Heat an oven-safe, non-stick pan (or well-seasoned cast iron pan) over medium heat. Add the vegetable oil.
Once the pan is hot, place the chicken breast-side-down and weigh it down with a heavy object like a foil-wrapped brick or a dutch oven. This ensures even contact with the pan for proper browning.
Cook the chicken on the stovetop for 15 minutes, checking and adjusting the heat every 5 minutes to prevent burning.
While the chicken is cooking, prepare the marinade by combining the olive oil, lemon juice, minced garlic, thyme leaves, smoked paprika, salt, and pepper in a bowl.
Remove the chicken from the pan and place it on a sheet pan. Turn off the heat, and drain the excess fat from the skillet.
Add the halved baby potatoes to the pan, cut side down. Add the quartered red onion.
Place the chicken on top of the vegetables, breast-side-up. Pour the prepared marinade evenly over the chicken.
Transfer the pan to the preheated oven and bake for 20 minutes, or until a meat thermometer inserted into the thickest part of the breast reads 165°F (74°C).
Remove the chicken from the pan with tongs, taking care not to tear the skin. Return the pan to the oven and continue to cook the potatoes for another 10 minutes. Let the chicken rest while the potatoes finish cooking.
To serve, plate the chicken with the potatoes, garnish with fresh parsley, and serve with lemon wedges.