Combine the water, ¼ cup Swerve Brown, ¼ cup salt, 1 teaspoon pepper, and the herbs in a medium saucepan. Bring to a boil over high heat and continue to cook, stirring, until the Swerve and salt are fully dissolved. Add the ice and stir until the ice is melted and the mixture cool. Pour into a large food storage bag, add the pork chops, then flip over a few times. Let sit at room temperature for 1 hour or refrigerate for up to 12 hours. If brining in the refrigerator, take out of the fridge about an hour before cooking.
Prior to cooking, combine 1/3 cup Swerve Brown with ½ teaspoon salt, ½ teaspoon pepper, the garlic powder, paprika, and cayenne pepper in a shallow bowl or on a plate. Remove the pork chops from the brine, discarding the brine, rinse with cold water and pat dry. Press the chops into the spice mixture, coating well on both sides.
Heat the oil in a heavy skillet over medium-high heat. Once the oil starts to shimmer, add the pork chops and cook for 3-4 minutes per side or until both sides are golden brown and the pork registers 145 degrees on an instant-read thermometer. Let the chops rest for 5 minutes before serving.
Make the Applesauce:
Melt the butter in a saucepan or skillet over medium-high heat. Add the rest of the ingredients and bring to a light boil. Reduce the heat to low, cover the pan, and let simmer for 10-15 minutes or until the apples are tender. Mash with a potato masher until chunky. Can be served warm or cold.