Pat chicken dry and place in a bowl. Add 1 tbsp olive oil, minced garlic, lemon zest from the lemon, smoked paprika, dried oregano, 1 tsp salt, and black pepper. Toss to coat and let sit at room temperature for 10–15 minutes while you preheat the oven to 425°F.

On a baking sheet, toss broccoli with the remaining 1 tbsp olive oil and 0.25 tsp salt. Spread into a single layer and roast in the preheated oven for 12–15 minutes until edges are browned and stems are tender-crisp. Stir once halfway through for even browning.

Meanwhile, heat a 10-inch ovenproof skillet over medium-high heat until hot. Add the chicken thighs, presentation side down (smooth side), and sear without moving for 4–5 minutes until golden-brown. Flip and sear the other side 2 minutes.

Pour chicken broth and the juice of the zested lemon into the skillet, scraping any browned bits with a wooden spoon. Stir in honey and red pepper flakes. Dot the cold butter around the skillet and spoon a little of the sauce over the chicken. Transfer skillet to the oven and bake 8–10 minutes until an instant-read thermometer inserted into the thickest part reads 165°F.

Remove skillet from oven and transfer chicken to a plate; tent with foil and rest 5 minutes. While chicken rests, return skillet to medium heat on the stove and simmer sauce 1–2 minutes to thicken slightly if needed. Toss roasted broccoli into the skillet to coat with a little sauce, or combine on a serving platter.

Slice or serve whole chicken thighs over the roasted broccoli, spoon remaining pan sauce over everything, and sprinkle with chopped parsley. Taste and add a pinch of salt or a squeeze of lemon if desired.