Pasta and Chicken Gratin

Cut backbones, wing tips, and second joints of wings from chickens, then cut each chicken into quarters. Put backbones, wing tips, second joints, and giblets (except livers) in a 6- to 8-quart pot with water, celery, carrot, onion, garlic, thyme, salt, and peppercorns and bring to a boil.

Add chicken quarters and return liquid to a boil, skimming off any foam, then reduce heat and simmer, uncovered, 10 minutes.

Remove from heat and let stand, covered, 40 minutes.

Transfer chicken quarters with tongs to a shallow baking pan. When chicken is cool enough to handle, remove meat from skin and bones, transferring meat to a cutting board and returning skin and bones to pot.

Cut chicken into 1-inch pieces and reserve in a large bowl. Boil stock 40 minutes, then pour through a fine-mesh sieve into a large bowl, discarding solids.

Let stand 5 minutes, then skim off fat and set aside 4 cups stock for making sauce. (Reserve remaining stock for another use.)

Put oven rack in middle position and preheat oven to 425F. Butter gratin dishes.

Heat butter (1 stick) in a 4-quart heavy pot over moderate heat until foam subsides, then add garlic and cook, whisking, 1 minute.

Add flour and cook, whisking, 1 minute.

Add milk and reserved stock (4 cups) in a slow stream, whisking, then bring to a boil, whisking. Reduce heat and simmer, whisking occasionally, until sauce is slightly thickened, about 10 minutes.

Remove from heat and stir in crme frache, salt, pepper, cayenne, 2 cups Gruyre, and 1/2 cup Parmigiano-Reggiano.

While sauce simmers, cook pasta in a 6- to 8-quart pot of boiling salted water , uncovered, until not quite al dente, 8 to 10 minutes (pasta should still be firm), then drain in a colander. Return pasta to pot, then add chicken and sauce, tossing to coat. Divide pasta mixture between gratin dishes.

Toss bread crumbs with remaining 4 cups Gruyre and 3/4 cup Parmigiano-Reggiano, then sprinkle evenly over pasta mixture.

Bake gratins until crumbs are golden brown and sauce is bubbling, 20 to 30 minutes.

Let stand 10 minutes before serving.

Cooks' notes:If using rotisserie chickens, pull meat from bones and reserve, then make stock by cooking skin and bones with celery, carrot, onion, garlic, thyme, salt, peppercorns, and 8 cups water 40 minutes total before straining. Chicken can be poached and stock can be made 1 day ahead and cooled completely, uncovered, then chilled separately, covered. Bread crumbs can be made 1 day ahead and kept in a sealed plastic bag at room temperature. Cheeses can be grated 1 day ahead and chilled separately in sealed plastic bags.