Duck à l'Orange

Trim off wing tips and flats; set aside.

Cut carcass into quarters.

Cover and chill leg, breast, and wing pieces.

Heat reserved duck skin in a large heavy pot over medium heat.

Cook, stirring, until about 2 tablespoons fat is rendered; discard skin.

Add giblets, wing tips and flats, carcass pieces, onion, and thyme sprigs.

Cook, stirring occasionally, until lightly browned, about 15 minutes.

Add celery, carrot, peppercorns, and 6 cups water.

Bring to a boil over high heat, skimming any foam that rises to the surface.

Reduce heat to medium; simmer duck stock for 1 hour.

Meanwhile, using a sharp knife, cut all peel and white pith from 1 orange; set peel aside.

Working over a medium bowl, cut between membranes to release segments into bowl; set aside.

Add orange peel to simmering stock.

Juice remaining 2 oranges and set juice aside.

Strain stock through a fine-mesh sieve into a medium bowl (you should have about 2 cups).

Transfer orange peel to a work surface; discard remaining solids in sieve.

Slice peel into thin strips (remove white pith for a more refined look, if desired); set aside.

DO AHEAD: Stock can be made 1 day ahead.

Cover and chill stock and peel separately.

Prick duck pieces all over with a sharp knife.

Season with salt and pepper.

Arrange them in a single layer in a large heavy skillet (use 2 if needed), skin side down, and cook over medium heat, occasionally pouring off fat from skillet into a heatproof bowl, until skin is deep golden brown, 18-20 minutes. (Cover and chill fat; save for cooking potatoes or stir-fried rice.).

Turn over duck pieces.

Cook breasts, skin side up, until an instant-read thermometer inserted horizontally into thickest part of breast registers 125°F for medium-rare, about 2 minutes.

Transfer breasts to a large rimmed baking sheet.

Continue cooking legs and wings until well browned on both sides and juices run clear when thigh is pierced with a fork, 10-15 minutes longer.

Transfer to sheet with breasts.

Pour off fat from skillet, leaving browned bits behind.

Preheat oven to 450°F.

Return skillet with browned bits to medium-high heat.

Pour in Port and cook, scraping pan with a wooden spoon (the browned bits will add extra flavor to the sauce), until reduced and syrupy, about 2 minutes.

Add reserved orange juice and duck stock; boil, stirring occasionally, until sauce is smooth and thickened, about 20 minutes.

Season sauce to taste with salt and pepper.

Cover and keep warm.

Place rimmed baking sheet with duck pieces in oven.

Bake until duck is just heated through, 5-8 minutes.

Pour warm sauce onto a deep platter.

Scatter orange segments and strips of peel over.

Top with duck pieces.