Place 1 cup of the broth and 1/2 cup of the corn in a food processor; process until corn is puréed.
Remove lid from a 6-quart Instant Pot®. Press [Sauté], and use [Adjust] to select "More" mode. When the word "Hot" appears, swirl in 1 1/2 teaspoons of the oil. Add half of chicken; cook 5 minutes, browning on all sides. Remove chicken from cooker. Repeat procedure with remaining half of chicken; remove from cooker. Carefully remove inner pot from cooker. Remove drippings from inner pot.
Return inner pot to cooker. Add remaining 1 1/2 teaspoons oil to cooker. Add onion and carrot; cook, stirring constantly, 2 minutes. Stir in 1 1/2 cups water and next 4 ingredients (through thyme). Stir in puréed corn mixture, remaining 2 1/2 cups broth, and remaining 1 cup corn. Return chicken thighs to cooker. Turn cooker off.
Close and lock the lid of the Instant Pot®. Turn the steam release handle to "Sealing" position. Press [Manual]; select "High Pressure," and use [-] or [+] to choose 23 minutes pressure cooking time. When time is up, open the cooker using Quick Pressure Release (page 4). Remove chicken from cooker; cool slightly.
Remove chicken from bones, discarding bones. Shred chicken into bite-sized pieces. Return shredded chicken to cooker. Stir in cilantro and next 4 ingredients (through black pepper). Turn cooker off; press [Sauté], and use [Adjust] to select "More" mode. Cook, uncovered, 5 minutes, or until thoroughly heated, stirring frequently. Ladle stew into 9 bowls; top with avocado and capers.
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