Preheat the oven to 375°F (190°C).
Spatchcock the chicken by removing the backbone, cracking the breast bone, and flattening it. Season both sides with kosher salt and pepper.
Heat a non-stick or cast iron pan over medium heat and add vegetable oil.
Place the chicken breast-side down in the pan and weigh it down with a foil-wrapped brick or Dutch oven. Cook for 15 minutes, checking the heat every 5 minutes.
While cooking, mix olive oil, lemon juice, garlic, thyme, smoked paprika, salt, and pepper to make the marinade.
Remove the chicken, drain the pan, and add halved potatoes and red onions. Place the chicken on top, pour the marinade over it, and transfer to the oven.
Bake for 20 minutes until the chicken reaches 165°F (74°C). Let the chicken rest while the potatoes finish cooking. Serve with parsley and lemon wedges.