Preheat the oven to 425 degrees F.

On a rimmed baking sheet, combine the chicken, 2 tablespoons olive oil, 2 finely chopped garlic cloves, 1/4 cup chopped parsley, 2 tablespoons chopped oregano, and a large pinch each of salt and pepper. Toss well to evenly coat the chicken. Arrange the lemons and smashed garlic cloves around the chicken. Add 1 slice of butter to each piece of chicken. Transfer to the oven and roast for 35-45 minutes, cooking until the chicken is cooked through and the lemons are charred.

To make the dressing, combine the remaining 1/3 cup olive oil, 3/4 cup parsley, 2 tablespoons oregano, the basil, olives, vinegar, and fish sauce, if using.

Remove the charred lemon slices and garlic cloves from the baking sheet. Finely chop the lemon slices, rind and all, discarding any of the seeds. Add half of the chopped lemon to the dressing. Finely chop/mash the garlic into a paste and stir it into the dressing. Season with crushed red pepper and salt. Taste, adding more of the lemon as desired.

Serve each piece of chicken with goat cheese and the dressing spooned over top.