Slice the pork loin into 1-inch thick chops.
In a medium pot, bring 4 cups water, lemon juice, honey and 1/2 teaspoon salt to a boil for 2 minutes.
Remove from heat, add 2 cups cold water. Pour the brine into a plastic container large enough for the chops. Add the chops, brine overnight.
Preheat oven to 350°. Place pecans on a baking sheet and bake for 5 minutes or until golden brown.
For the stuffing: In a large skillet over medium heat, melt the butter. Add the apple slices, brown sugar, 1/4 teaspoon salt and 1/4 teaspoon pepper. Sauté until tender. Remove from heat and allow to cool for 5 minutes. Add the chopped pecans and goat cheese.
Remove the chops from the brine.
Slit each chop horizontally to create a large hole for the stuffing.
Spoon the stuffing into the chops. Season each chop with salt and pepper to taste.
In a large skillet over medium-high heat, sear each chop in extra virgin olive oil.
Place chops on a baking pan and bake for 20-30 minutes until internal temperature is 155-160°.