Pat the chicken thighs (or breasts) dry with a paper towel and season with kosher salt. Let it sit out while you prep the rest of the ingredients.
Whisk together the balsamic, honey, olive oil, shallots, salt and pepper. Place the chicken in a re-sealable plastic bag and pour in the marinade. Seal the bag and make sure all the chicken is coated. Let sit at least 30 min and up to overnight in the fridge. Take out of the fridge 30 minutes before placing in hot oven.
Meanwhile, pit the cherries and set aside.
To cook chicken: about 30 min before, take it out of the fridge so chicken can come to room temperature. Preheat oven to 400 degrees F. Place chicken thighs (or breasts) skin side up in a shallow roasting dish or cast iron skillet. Nestle the rosemary springs in between the chicken pieces of top with the pitted cherries, moving them around so they fall in between the chicken pieces leaving as much as the skin exposes as possible. The pour the marinade over the chicken. The marinade should generously cover the bottom of the pan.
Slide the pan into the oven and rotate every 10-12 minutes.
Cooking times; for breasts: cook 20 minutes; for thighs: cook 45minutes. If using both remove the breasts while the dark meat continues cooking.
When the dark meat is tender at the bone and cooked through, return breasts to the pan and increase oven to 450 F. Let the sauce reduce and the chicken skin get dark and crispy, about 12 minutes. Move the cherries around again in needed to expose more chicken skin. Brush the chicken with the marinade from the pan every 3-4 minutes to glaze them.
Serve warm, with crunchy sea salt and freshly grinded black pepper.