
Place the chicken in a large pot with the onion, garlic bulb, bay leaves, oregano, celery, red pepper, and salt. Add water to cover and bring to a simmer. Skim off any foam that forms on top, then reduce the heat and let the chicken gently poach for 45 minutes, occasionally skimming.
Once the chicken is cooked, remove it from the heat and let it cool slightly. Pull the meat from the bones and set it aside. Save the poaching liquid and vegetables, and squeeze the garlic from its skin.
Crush the allspice berries using a pestle and mortar. Heat half the vegetable oil in a frying pan over high heat and add the crushed allspice, squeezed garlic, reserved vegetables, tarragon, nutmeg, and 150ml of the poaching liquid. Let it simmer for 10–15 minutes before adding lime juice.
Blend the sauce with a hand blender until smooth. Taste it and adjust seasoning with salt and pepper. If too thin, reduce further in a pan until it thickens. Mix the sauce with the shredded chicken and keep warm.
For the garnish, heat the remaining oil in a pan on medium heat. Add the diced onion and chopped garlic, cooking until soft. Stir in the cumin and coriander stalks, then add the drained beans and a ladle of chicken cooking liquid. Simmer for 10 minutes until the liquid evaporates, then mix in the lettuce and coriander leaves.
To serve, place some beans on a tortilla, followed by the pulled chicken and sauce. Top with a spoonful of soured cream and some ricotta cheese if desired. Roll up the wraps, slice them in half, and serve immediately.