Step 1

In a large saucepan, cover the chicken breast halves with the stock and 1 quart of water and bring to a boil. Simmer over moderately low heat, turning the chicken occasionally, until an instant-read thermometer inserted in the thickest part of each piece registers 160°, 30 to 35 minutes. Using tongs, transfer the chicken to a plate to cool. Discard the skin and bones. Shred the meat and season generously with salt and pepper. Transfer 2 cups of the chicken cooking broth to a large heatproof measuring cup and reserve the remaining broth for another use.

Step 2

Wipe out the saucepan and melt the 6 tablespoons of butter in it. Whisk in the flour and cook over moderate heat, whisking constantly, until bubbling and just starting to change color, about 2 minutes. Gradually whisk in the milk and the 2 cups of cooking broth and bring to a boil. Simmer over moderately low heat, whisking frequently, until the sauce is thickened and no floury taste remains, about 10 minutes. Remove the sauce from the heat and season generously with salt and pepper. Let cool slightly.

Step 3

Preheat the oven to 375°. Grease a 9-by-13-inch baking dish. Line the dish with 6 slightly overlapping tortillas. Spread one-third of the sauce over the tortillas, then top with 1 cup of the cheese and half each of the chicken, chiles and onion. Repeat the layering with 6 more tortillas, one-third of the sauce, 1 cup of the cheese and the remaining chicken, chiles and onion. Lay the remaining 6 tortillas on top and spread the remaining sauce over them.

Step 4

Bake the enchiladas for about 45 minutes, until the filling is bubbling. Sprinkle the remaining 1 cup of cheese on top and bake for 15 minutes more. Turn on the broiler and broil for 1 to 2 minutes, until lightly browned in spots. Let the enchiladas stand for 20 minutes. Garnish with cilantro leaves and jalapeño slices and serve.