Preheat the oven to 425°F. Pat the chicken thighs very dry with paper towels (this helps the skin crisp). Season both sides of the thighs with 1 tsp kosher salt and 3/4 tsp black pepper (reserve the rest of the salt and pepper for the broccoli and finishing).

On a rimmed baking sheet toss the broccoli florets with 1 tbsp olive oil, 1/2 tsp kosher salt, 1/4 tsp black pepper, and red pepper flakes (if using). Spread in a single layer and put the sheet into the oven to roast for 12–15 minutes, until the edges are browned and tender-crisp. You'll roast the broccoli while you sear and then finish the chicken so timing overlaps.

Heat a 12-inch ovenproof skillet over medium-high heat. When hot, add 2 tbsp olive oil. Place the chicken thighs skin-side down and press gently to ensure even contact. Sear until the skin is deep golden-brown and much of the fat has rendered, 6–8 minutes. Flip and sear the other side 2–3 minutes.

Reduce heat to medium, push the thighs to the sides and add the butter, minced garlic, smoked paprika, and dried oregano. Cook the garlic 30–45 seconds until fragrant (don’t let it burn). Squeeze in the lemon juice and scrape any browned bits from the pan. Spoon the sauce over the thighs, then transfer the skillet to the oven and bake 12–15 minutes, until an instant-read thermometer inserted into the thickest part reads 165°F.

If the broccoli is done before the chicken, pull it out and toss with lemon zest (from the zested lemon), the remaining 1/2 tsp kosher salt and remaining 1/4 tsp black pepper. When the chicken is out of the oven, transfer thighs to a cutting board and rest 5 minutes so juices redistribute.

Spoon any pan sauce over the chicken, sprinkle with chopped parsley, and serve alongside the roasted broccoli. Taste and adjust with more lemon or salt if desired.