In a large bowl, whisk together the water and the salt until the salt dissolves. Add the rosemary and thyme. Place a gallon-sized ziplock bag in a large bowl. Place the pork chops in the bag, and fill the bag with the brine. Seal it, pressing out as much air as possible, and place the bowl with the bag in the refrigerator. Allow the pork chops to brine for a minimum of 1 hour, or up to overnight.
For the cranberries, heat the olive oil in a medium saucepan over medium heat and add the cranberries, maple syrup, orange zest, and rosemary. Sauté until the cranberries begin to release their juice and wrinkle slightly, about 10 to 15 minutes, stirring every 3 minutes or so. Remove from heat and set aside.
For the sweet potatoes, bring the sweet potatoes, bone broth, water, and salt to a boil in a large pot over medium high heat. Reduce the heat to medium low and continue boiling until the sweet potatoes are soft and tender when poked with a fork, about 10 to 15 minutes. Reserve 1/2 cup of the boiling liquid, and drain the rest, reserving the sweet potatoes. Place the sweet potatoes in a blender or food processor and add 1/3 cup of the reserved liquid. Blend until smooth and velvety, adding the rest of the reserved liquid if needed.
For the pork chop, preheat the oven to 400 degrees Fahrenheit. Set a large cast iron skillet in the oven to preheat it.
Remove the pork chops from the bag, rinse thoroughly, and pat them dry. Coast the pork chops with the olive oil and sprinkle them with some sea salt and black pepper.
Use oven mitts to transfer the hot skillet to the stovetop over medium high heat. Sear one side of the pork chops until golden, about 5 minutes. Flip the pork chops, remove the skillets from the stovetop, and immediately place them in the oven.
Roast until the thickest part of each pork chop reaches 145 degrees Fahrenheit. Serve immediately with the sweet potato purée and sautéed cranberries.