Heat the oven to 375°F (190°C). Season the chicken with 1 teaspoon salt and the black pepper.
Heat oil in an ovenproof skillet over medium-high heat. Brown the chicken skin-side down for 8 to 10 minutes, then turn and cook 4 minutes more. Transfer to a plate.
Make the Sauce:
Pour off excess fat, leaving 1 tablespoon in the skillet. Add butter and garlic and cook over low heat for 45 seconds without browning.
Stir in milk, cream, coriander, and remaining salt. Bring only to a gentle simmer.
Finish:
Return the chicken and any juices to the skillet. Bake uncovered for 20 to 25 minutes, until the thickest pieces reach 175°F (80°C).
Rest 5 minutes, scatter with parsley, and spoon the garlic sauce over the chicken.
Notes
Dark meat stays juicy during the skillet-and-oven method, but a small whole spatchcocked chicken also works.
For a lighter sauce, replace the cream with additional whole milk.