Place a 6-qt Instant Pot on Saute setting. Add oil. When oil is hot, add shallots and garlic. Cook 6 to 8 Minutes or until tender and starting to brown, stirring occasionally. Transfer shallots, garlic, and all but 1 Tbsp oil to a small bowl. Season chicken with 1/2 tsp salt. Brown chicken, in batches, in reserved oil in pot, turning to brown evenly. Return all chicken to Instant Pot. Top with green beans.
Add next seven ingredients (through cardamom) to shallot mixture in bowl. Spoon half of the mixture over chicken and beans in pot. Add broth. Sprinkle remaining 1/4 tsp salt over all. Lock lid in place. Set Instant Pot on High Pressure to cook 8 Minutes. Turn off Instant Pot; let stand 15 Minutes to release pressure naturally. Release any remaining pressure. Open lid carefully. Remove chicken and beans from pot to a serving platter. Top with remaining shallot mixture.