In a large pot, bring water to a boil and cook the chicken pieces until fully cooked, about 25-30 minutes. Remove the chicken from the pot and set aside. Reserve 1 cup of the cooking liquid.
Allow the chicken to cool, then shred or cut into bite-sized pieces.
In a large skillet, heat the vegetable oil over medium heat.
Add the finely chopped onion and cook until softened and translucent, about 5 minutes.
Stir in the minced garlic and cook for another 2 minutes until fragrant.
In a bowl, combine the finely chopped walnuts, red wine vinegar or apple cider vinegar, ground coriander, ground cumin, paprika, dried thyme, dried oregano, black pepper, salt, and reserved chicken cooking liquid (or chicken broth). Mix well to create a smooth sauce. If the sauce is too thick, add a little more water or broth.
Add the shredded chicken to the skillet with the onion and garlic mixture. Stir to combine.
Pour the walnut sauce over the chicken and mix thoroughly.
Reduce the heat to low, cover the skillet, and let the Satsivi simmer for 20-30 minutes, allowing the flavors to meld. Stir occasionally.
Garnish with chopped fresh cilantro and parsley.
Enjoy your meal!