Preheat oven to 425°F. Pat chicken thighs dry with paper towels; season both sides with 1 tsp kosher salt, 1/4 tsp black pepper, paprika, and half the oregano. Toss halved baby potatoes with 1 tbsp olive oil and 1/2 tsp kosher salt in a bowl.

Heat 1 tbsp olive oil in a 12-inch ovenproof skillet over medium-high heat. Add cut-side-down potatoes in a single layer and cook, undisturbed, until the cut sides are golden brown, about 6–8 minutes. Use tongs to flip and cook 2 more minutes. Transfer potatoes to a bowl and set aside.

In the same skillet, add a touch more oil if needed and arrange the seasoned thighs in a single layer. Sear 3–4 minutes per side, until golden (they will not be fully cooked). Push chicken to one side of the skillet.

Reduce heat to medium, add minced garlic and remaining oregano to the empty side of the skillet and cook 30–45 seconds until fragrant. Stir in lemon juice and scrape up browned bits with a spatula. Return potatoes to the skillet, nestling them around the chicken.

Transfer the skillet to the preheated oven and roast 12–15 minutes, until chicken reaches an internal temperature of 165°F and potatoes are fork-tender. If top browning is desired, broil 1–2 minutes—watch closely.

Remove skillet from oven, add baby spinach over the hot chicken and potatoes and let wilt for 1–2 minutes; toss gently to coat in pan juices. Taste and adjust seasoning with remaining 1/2 tsp kosher salt and remaining black pepper if needed. Sprinkle with chopped parsley and serve hot, spooning pan sauce over each portion.