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1
Mix water, salt, and brown sugar in a saucepan, stirring to dissolve salt and sugar. Add bay leaves, rosemary, 1 teaspoon black pepper, and thyme; bring to a boil. Reduce heat to low and simmer brine for 5 minutes. Let brine cool to room temperature.
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2
Place pork roast into a large nonreactive bowl, pour brine over pork, and cover; marinate in refrigerator for 12 to 24 hours.
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3
Heat olive oil in a skillet over medium heat; cook and stir apple and shallots into hot oil until shallots are soft, about 5 minutes. Remove from heat, let cool to room temperature, and mix spinach, walnuts, egg, and goat cheese into apple mixture. Season stuffing with salt and black pepper.
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4
Preheat oven to 400 degrees F (200 degrees C).
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5
Remove pork from brine and discard used brine. Cut roast lengthwise down the center to within about 1 1/2 inches of the bottom and open the roast like a book. Spoon apple stuffing onto one side of meat and fold the other half over the stuffing. Tie the roast closed in 4 or 5 places with kitchen twine. Set roast on a rack placed into a roasting pan.
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6
Roast in the preheated oven until an instant-read thermometer inserted into the center of the stuffing reads 145 to 150 degrees F (63 degrees C to 65 degrees C), about 1 hour and 15 minutes.
