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1
Heat the oven to 400 degrees.
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2
Prepare the duck: Poke the skin all over the duck with a fork. Season the duck all over with 1 1/2 teaspoons salt and one-fourth teaspoon pepper, rubbing the seasoning over the skin.
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3
In a small bowl, stir together the celery, onion, cinnamon sticks, star anise and 1 tablespoon olive oil. Stuff the mixture into the cavity of the duck and tie the legs together with the tail to prevent the stuffing from falling out.
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4
Heat a large saute pan over medium-high heat and add the remaining tablespoon oil. Brown the duck, turning every few minutes to color each side evenly and well, about 20 minutes total.
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5
Place the duck and any juices in a baking pan and roast, basting every 15 minutes, until the juices run clear when you prick the thigh, about 2 hours.
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6
Remove the duck and set aside to rest 20 to 30 minutes before carving.
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7
While the duck is in the final hour of roasting, make the kumquat sauce. Place the honey in a 2-quart heavy-bottom saucepan over high heat. Bring the honey to a boil and cook just until it begins to darken and caramelize. Immediately remove the pan from heat and add the vinegar and orange juice, stirring to combine.
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8
Cook over medium heat until the liquid is reduced by three-fourths, 20 to 25 minutes. Stir in the butter and kumquat slices and simmer gently for 5 minutes, stirring occasionally to allow the flavors to marry. Remove from heat and serve with the duck.
