In a bowl of a food processor or a blender combine walnuts, cilantro, chillies, garlic, lemon juice and 1/2 cup of chicken stock and process until you have a smooth paste. Set aside.
Heat a tablespoon of olive oil in a large pan and brown seasoned with salt and pepper chicken pieces on both sides over medium heat. Work in batches to avoid overcrowding. Remove browned chicken on a plate and set aside.
Discard all but 2 tablespoons of fat from the pan, then add chopped onion and cook for 5 minutes over low heat until tender but not colored.
Add flour and stir, then add chicken stock gradually while stirring to combine and turn the heat up to bring to a boil, then turn it down, add the satsivi paste and stir to combine.
Return chicken to the pan with, bring the sauce to a boil, then turn heat down and simmer for 30 minutes uncovered until the sauce is the consistency of the sauce is thicker than heavy cream.
Sprinkle with chopped cilantro and tarragon before serving. Serve with rice and flatbread.