Preheat oven to 450 degrees F. Mince garlic with a pinch of salt. Then whisk together with 1/2 teaspoon of salt, 1/4 teaspoon pepper, 2 tablespoons oil and 1 tablespoon lemon juice. Pat chicken dry and coat with lemon-garlic mixture.
Heat 1 tablespoon butter and remaining oil in a 12-inch heavy skillet over medium-high heat and brown chicken in 2 batches, skin side down, until golden and crisp. Then remove to a baking dish, skin side up. Arrange asparagus alongside chicken. Pour off fat from skillet. Add broth and remaining tablespoon lemon juice and boil until reduced by half, about 2 minutes. Whisk in remaining tablespoon butter and oregano, and then pour over chicken and asparagus.
Roast chicken in oven until cooked through, about 20 minutes. Add a grating of freshly milled black pepper and serve, garnished with parsley and lemon wedges.
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