Prepare the brine: Place 5 cups of cold water in a large bowl.
Next heat 1/2 cup water, 2 tablespoons salt, 1 tablespoon brown sugar, and 4 of the sage leaves in a small saucepan; cook over medium high heat, stirring to dissolve the sugar and salt. Add salt mixture to the bowl of cold water.
Place the pork chops in the brine for at least 10 minutes. Chop 3 of the sage leaves and set aside.
Now toss together (either in a large bowl or directly on your baking sheet) the squash, 2 tablespoons olive oil, and remaining 5 sage leaves. Season with nutmeg and about 1/2 teaspoon of salt. Roast until tender about 20 to 25 minutes (at 425 degrees F).
Drain the pork chops and pat them dry with paper toweling. In a large skillet, heat the remaining 1 tablespoon of oil over medium high heat. Cook pork chops to an internal temperature of 140 degrees, about 5 to 7 minutes per side (you can insert your meat thermometer in the side for a true reading).
To the skillet, add the chicken broth and remaining 1 tablespoon brown sugar, simmer, stirring, until reduced by half. This takes about 3 minutes. Remove from heat and squeeze in the lemon juice, add the reserved chopped sage, and any salt to taste.
To serve: Place a pork chop on each of 4 plates. Drizzle with the pan sauce. Serve squash on the side.