Pat the chicken thighs dry with paper towels, then season both sides with 1 tsp kosher salt and 0.5 tsp black pepper. Zest the lemon and juice it to measure about 2 tablespoons. Trim broccoli into uniform florets so they cook evenly.

Heat a 10–12 inch skillet over medium-high heat until hot, then add 2 tbsp olive oil and swirl. Add the thighs in a single layer (work in two batches if needed) and sear without moving for 4–5 minutes until the undersides are deep golden. Flip and cook another 3–4 minutes until the second side is golden but not fully cooked through. Remove thighs to a plate (they will finish cooking in the sauce).

Reduce heat to medium, add the minced garlic to the skillet with any rendered fat and cook, stirring, for 30 seconds until fragrant (don’t let it brown). Pour in 1/2 cup chicken broth and the lemon juice, using a wooden spoon to scrape up browned bits from the pan. Add the lemon zest and bring the liquid to a gentle simmer.

Nestle the seared chicken thighs back into the skillet, spooning some sauce over them. Tuck the broccoli florets around the chicken. Cover the skillet and simmer gently for 6–8 minutes, until the broccoli is tender-crisp and the chicken reaches an internal temperature of 165°F (use an instant-read thermometer) or juices run clear.

Remove the lid, turn heat up to medium-high for 1 minute to reduce the sauce slightly if it’s thin. Stir in the 2 tbsp cold butter one piece at a time, swirling the pan to create a glossy sauce. Taste and season with the remaining 0.5 tsp kosher salt and 0.25 tsp black pepper if needed. Sprinkle with red pepper flakes if using.

Transfer chicken and broccoli to plates or serve family-style from the skillet. Spoon extra pan sauce over the top and scatter chopped parsley for freshness. Serve with rice, mashed potatoes, or crusty bread to soak up the sauce.