Heat 2 tablespoons of butter in a large pot or Dutch oven. Pat the chicken thighs dry using a paper towel. Season with salt and pepper and place the chicken on the melted butter in the pot. Add the onions on top and allow the chicken to sear for 3-4 minutes until lightly browned.
Flip the chicken over and sear the other side for another 3-4 minutes. Add the spices, bay leaves and cinnamon stick on top of the chicken and onions. Cover everything with 6 cups of water, bring to a boil and then simmer for 15 minutes. Skim any fat that rises to the top and add the drained chickpeas. Cook for 15 more minutes.
Remove the chicken thighs from the cooked broth, shred it using your hands or two forks, then return to the pot.
Heat the butter in a medium pot. Add the dry moghrabieh and season salt and caraway. Cover with 3 cups of water, bring to a boil and simmer for 20 minutes, until tender. Remove from heat and fluff with a fork.
Serve the moghrabieh warm with a couple ladles of the chicken broth. Garnish with parsley, if desired.