Brine the pork:

Combine 2 cups of the apple cider or juice with the salt, brown sugar, garlic, and thyme in a 3- to 4-quart saucepan and bring to a boil over high heat, stirring so the salt and sugar dissolve, about 3 minutes. Add the remaining apple cider or juice and cool to room temperature. Transfer to a large container, add the pork, cover, and refrigerate for at least 8 hours and up to 18 hours.

Roast the pork:

Position a rack in the center of the oven and heat the oven to 450°F. In a small bowl, mix the maple syrup, mustard, thyme, and pepper. Drain the pork and pat dry with paper towels. Brush the pork all over with the mustard mixture.

In a medium bowl, toss the fennel and apple with the oil, salt, and a few generous grinds of pepper. Scatter the mixture in the bottom of a large roasting pan (large enough to hold the pork with a couple of inches of space around the perimeter). Put the pork, fat side up, on top of the fennel and apples. Roast the pork until the crust just starts to brown, about 15 minutes. Reduce the heat to 350°F and continue cooking until an instant-read thermometer inserted into the thickest part of the loin registers 145°F, 30 to 50 minutes more.

Let rest for 10 minutes and then thinly slice a quarter to a third of the pork. Serve, topped with the fennel, apple, and juices. Allow the remaining pork to cool to room temperature, wrap well with foil, and refrigerate for up to 5 days.