Pat the chicken thighs completely dry with paper towels, then season both sides generously with the salt and pepper
Heat the olive oil in a large skillet over medium-high heat until shimmering, then lay the thighs in skin-side down and let them sear undisturbed for 6 to 7 minutes, until deeply golden and releasing easily from the pan
Flip the thighs and sear the second side for 5 to 6 minutes, then transfer them to a plate and set aside
Lower the heat to medium, add 1 tablespoon of the butter to the same pan, then stir in the garlic and cook for about 30 seconds, just until fragrant
Pour in the chicken broth, scraping up the browned bits from the bottom of the pan, then stir in the lemon juice, lemon zest, thyme, and red pepper flakes if using
Nestle the chicken thighs back into the pan skin-side up, spoon a little sauce over the tops, and simmer for 8 to 10 minutes, until the chicken reaches 165°F internally
Remove the pan from the heat, swirl in the remaining 2 tablespoons of butter until the sauce turns glossy, then scatter the parsley over the top
Let the chicken rest in the pan for 5 minutes before serving so the juices settle back into the meat
Notes
For the crispiest possible skin, bring the chicken to room temperature for 15 minutes before searing and resist moving it until it releases naturally from the pan. Leftovers keep in the fridge for up to 4 days; reheat in a 375°F oven, not the microwave, to keep the skin crisp.