Start by prepping your chicken: wash the chicken and thoroughly pat dry using paper towels. Sprinkle the chicken with a few pinches of salt and pepper on both sides.
To a large pot, heat 2 tablespoons of oil over moderately medium to high heat. When the oil is hot, place the chicken, skin-side down and cook until the skin is crispy and browned, about 3 to 5 minutes. Flip the chicken, using a pair of tongs, and cook for an additional minute or so. You want to avoid overcrowding the pot, so you most likely will have to do this in batches. Remove the chicken from the pan and set it aside in a bowl.
You may find that the chicken's skin has released a lot of grease. We don't want all of that in the dish so dump out most of it, leaving about 1 tablespoon (eyeball this measurement). Place the pot over medium heat and when hot, add the potatoes, cooking them on each side until browned and crispy, about 1 minute. Remove them from the pan and set aside.
Throw in the shallot and cook until translucent, about 3 minutes. Add the garlic and cook until fragrant, about 1 minute. Next, add the cumin, coriander and fresh thyme. Pour in the red wine vinegar and using a spoon, deglaze the bottom of pan, scraping up any browned, crispy bits. Add the swiss chard, lemon zest and chicken stock. Add the chicken and potatoes back to the pot, being sure to nestle them into the mixture.
Bring the chicken mixture to a simmer and turn the heat to low; cover the pot and cook for 45 minutes, until the potatoes and chicken are cooked. Mix in the heavy cream and salt the mixture to taste (I added about 1 teaspoon). Cook for an additional 10 to 15 minutes. Divide between bowls and top with a sprinkling of fresh Italian parsley.