Preheat the oven to 425 degrees F. Combine 1/2 cup water, 2 tablespoons salt, 1 tablespoon brown sugar and 4 sage leaves in a small saucepan over medium-high heat, stirring, until the sugar and salt dissolve. Pour the mixture into a large bowl and add 5 cups cold water. Submerge the pork chops in the brine and refrigerate 10 minutes.
Chop 3 sage leaves; set aside. Toss the remaining 5 sage leaves with the squash, 2 tablespoons olive oil, the nutmeg and 1/2 teaspoon salt. Spread on a baking sheet and roast until tender, 25 to 30 minutes.
Heat the remaining 1 tablespoon olive oil in a large nonstick skillet over medium-high heat. Drain the pork and pat dry. Add to the skillet and cook until a meat thermometer inserted sideways into the center registers 140 degrees F, 5 to 7 minutes per side. Divide among 4 plates.
Add the chicken broth and the remaining 1 tablespoon brown sugar to the skillet; simmer, stirring, until reduced by half, about 3 minutes. Remove from the heat and add the lemon juice, the reserved chopped sage, and salt to taste. Drizzle the pork with the sauce and serve with the squash.
Photograph by Antonis Achilleos
Recipe courtesy Food Network Magazine