In a 6-to 8-quart pot heat vegetable oil over medium-high heat. Add onions, celery, and chiles: cook and stir for 4 to 5 minutes or until softened. Stir in ancho powder; cook and stir for 1 minute.
Add broth, corn, chicken, and black pepper. Bring to boiling.
Fill hot clean quart canning jars halfway with chicken and vegetables. Add broth, leaving a 1-inch headspace. Wipe jar rims; adjust lids and screw bands.
Process filled jars in a pressure canner at 10 pounds pressure for a weighted gauge canner or 11 pounds pressure for dial-gauge canner for 75 minutes, adjusting for altitude. Allow the pressure to come down naturally. Carefully remove canner lid; cool jars in canner for 10 minutes. Remove jars from canner; cool on wire racks. Check lids for seal after 24 hours.
To serve, place contents of one jar in a medium saucepan. Bring to a rapid boil. Boil, covered, for 10 minutes (add 1 additional minute for each 1,000 feet of elevation). Remove saucepan from heat. Add 1/2 cup instant mashed potato flakes and two 3/4-ounce slices American cheese, torn, to soup, stirring until cheese melts.
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10 g fat
(4 g saturated fat,
2 g polyunsaturated fat,
4 g monounsaturated fat),
47 mg cholesterol,
735 mg sodium,
21 g carbohydrates,
2 g fiber,
5 g sugar,
19 g protein.