For the chicken stock, place all ingredients in the water, bring to a boil, cover and let simmer for 40 minutes. Turn off heat and let cool before working on the chicken.
To prepare for this stew, pick the leaves off the stems and roughly chop them. If they're chopped finely, they will become stringy, so stay with the rough chop.
You will need about four bunches to make enough to serve four. They wilt like spinach. Set aside the chopped leaves.
Finely dice the onion, jalapeno and garlic and saute in the pot with the tablespoons of olive oil. Finely chop the cilantro and add to the pot.
Once all wilted, add the chicken stock and start adding the mallow leaves a handful at a time, alternating with the lemon juice until all the leaves are in. Stir them in the stock to submerge them.
Add salt and pepper and the pulled chicken and let simmer for 10 minutes on low heat. Serve with steamed rice and vinegar-marinated onions with the vinegar (about 2 tablespoon per plate).