Preheat the oven to 375°F (190°C).
Pat the hen dry inside and outside. Season the within with 2 teaspoons salt and the pepper. Place as most of the orange and lemon quarters, garlic cloves, and herb sprigs within the cavity as will match. Cross the legs one over the opposite or tie them along with kitchen string to carry the contents inside. Tuck the wings beneath the hen as if it was placing its arms behind its head. Squeeze a lemon quarter over the the hen and rub the juice into the pores and skin, then sprinkle the hen with the remaining 1 teaspoon salt.
Place the hen, breast aspect up, in a roasting pan. Toss any remaining orange and lemon quarters, garlic, and herb sprigs within the pan. Roast till the hen’s juices run clear when a thigh is pierced with a fork or an instant-read thermometer registers 160°F (71°C) when inserted into the thickest a part of a thigh, 1 1/2 to 2 hours, relying on the scale. Switch the hen to a slicing board, cowl loosely with aluminum foil, and let relaxation for 10 minutes.
Whereas the hen rests, pour 1 cup inventory into the roasting pan and stir to scrape up any browned bits from the underside. Pressure the pan juices via a fine-mesh sieve right into a saucepan and place over low warmth. Add the butter and the remaining 3 cups inventory and swirl the pan gently till the butter melts. Sprinkle 1 tablespoon of the flour over the liquid and whisk till it dissolves and the juices have thickened a little bit, 3 to five minutes. If a thicker sauce is desired, sprinkle the remaining 2 tablespoons flour, or extra as wanted, and whisk once more.
Squeeze the juice from the orange and lemon quarters into the pan and cook dinner, stirring, till the juices have thickened a little bit extra and are shiny, about 5 minutes. The pan sauce needs to be thinner than a gravy and simply flippantly coat the again of a spoon. Stir within the chopped thyme. Style and alter the seasoning. (You will have ample pan sauce, nevertheless it’s beautiful spooned over rice or potatoes or nearly the rest you’ll be able to assume to placed on the identical plate as this citrus roast hen.)
Carve the roast hen and prepare on a platter. Serve with the nice and cozy juices on the aspect.