Potato- and Chorizo-Stuffed Ancho Chiles

Rinse chiles, then cover with cold water in a bowl and soak, weighted with a sieve (to keep submerged), until completely rehydrated (most will turn a brighter red), about 8 hours. Do not drain chiles.
Put oven rack in middle position and preheat oven to 350°F.
Remove 1 chile from soaking liquid and, working over chile bowl and sieve, cut a slit down one side with scissors and let interior liquid and loose seeds drain into sieve. Carefully cut out seedpod, leaving stem intact and letting any easily loosened seeds fall into sieve, then discard seedpod. Repeat with remaining chiles, arranging seeded chiles, cut sides up, in 1 layer in a 13- by 9- by 2-inch (3-quart) baking dish.
Reserve 1 cup chile-soaking liquid for sauce. Turn chile seeds out of sieve into a shallow baking pan and spread evenly, then toast in oven, stirring occasionally, until dry, fragrant, and a few shades darker, 8 to 10 minutes. Cool seeds in pan on a rack, then finely grind in grinder (you will have about 1 tablespoon).
Purée tomatoes, including juice from can, in a blender with reserved soaking water, ground chile seeds, and 1/2 teaspoon salt until smooth, then transfer to a 3-quart heavy saucepan and boil, stirring occasionally, until sauce is thickened slightly and reduced to about 2 cups, 5 to 7 minutes.
Peel potatoes and cut into 1/3-inch cubes (about 2 1/2 cups). Cook in a 3-quart pot of boiling salted water until tender but not falling apart, 6 to 8 minutes. Drain in a colander and rinse under cold water to stop cooking.
Stir together potatoes, chorizo, cheese, and 1/4 teaspoon salt in a bowl, then fill chiles generously with stuffing (about 1/2 cup each; slit will not close over it). Pour sauce around (not over) chiles, then cover dish with foil and bake until sauce is bubbling all over, 35 to 45 minutes.