Preheat the oven to 400F and a large skillet or braiser to medium heat.

While preheating, prep the leeks. Remove any tough outer stems/leaves and cut the leeks in half lengthwise, then thinly slice into half-moon shapes. Add the leeks to a bowl and fill with water. Swish the leeks around in the water and let sit for a few minutes; any grit or sand will sink to the bottom. Remove the leeks carefully to not disturb the dirt and let dry on a clean kitchen towel.

When the pan is hot, add a drizzle of olive oil and two tablespoons of the butter. Sprinkle the chicken very liberally with salt and pepper and add the thighs cut side down to the pan. Let the chicken cook undisturbed for 8-9 minutes until the chicken skin is brown and crispy. Flip the chicken and cook for 5 minutes more, then remove to a plate.

Add the leeks and garlic cloves to the chicken drippings. Stir for two minutes, then add the chicken stock. Stir to release any chicken from the bottom of the skillet, then add the chicken skin-side up to the sauce. Add the lemons cut-side up to the sauce between the chicken pieces.

Roast the dish uncovered for about 30 minutes until the sauce has reduced slightly and the lemons have browned. Remove from the oven and squeeze a bit of the lemon juice in to the sauce. Taste the sauce and add a few pinches of salt to your preference, then swirl in the remaining butter. Sprinkle with any fresh chopped herbs you'd like.