One day in advance, combine the water, salt, sugar, soy sauce, peppercorns, ginger, anise, and bay leaves in a deep baking dish large enough to hold the pork and stir to mix. Add the pork; if it is not covered, add more water. Cover and refrigerate overnight.
Preheat the oven to 375 degrees F. Rinse the pork thoroughly with cold water, pat dry, and season with the ground pepper to taste. Heat a large skillet over high heat, add the oil, and swirl to caot the bottom of the pan. When the oil shimmers, add the pork and brown on all sides. Transfer the pork to a roasting pan and roast just until the pork is hot through to the center (about 125 degrees F internal temperature), 25 to 30 minutes. The interior of the pork will remain pink.
Allow the pork to rest for 10 minutes and cut into 1/4-inch slices. Divide the gingered sweet potatoes among 4 plates, surround with the pork, and add the five-spice apples. Garnish with the chives, drizzle with the chile oil, and serve.
Heat a small saucepan over medium heat. Add 1 tablespoon of the butter and swirl to coat the bottom of the pan. Add the garlic and ginger and saute, stirring occasionally, until the garlic is brown, 3 to 4 minutes. Add the cream and reduce by one-third over low heat, about 10 minutes. Keep warm.
Meanwhile, combine the sweet potatoes in a large saucepan with enough water to cover them completely. Bring to a boil over high heat and cook until they can be pierced easily with the tip of a knife, 20 to 30 minutes. Drain and trasnfer to a food processor. Add the cream and process until well blended. Add the remaining butter, season with salt and pepper, and puree until smooth. Transfer the potatoes to a bowl, correct the seasonings, and serve.
For the Five-Spice Apples: Heat a medium skillet over medium heat. Add the oil and swirl to coat the bottom of the pan. When the oil shimmers, add the onion and saute, stirring, until brown, about 8 to 10 minutes.
Add the five-spice powder, brown sugar, apples, and juice. Stir, season with salt and pepper to taste, and cook until the liquid is reduced by half, about 12 minutes. The apples should retain their shape and some liquid should remain in the pan; do not overcook. Stir in the butter and correct the seasonings. Serve warm.
For the Chile Oil: In a medium skillet, combine the chile powder, cumin, and salt, and heat over medium heat just until the mixture begins to smoke. Whisk in the oil and remove from the stove.
Allow the chile oil to cool, transfer it to a glass jar, and let stand overnight. Cover and use or store. The oil will separate from the solids; use the red oil only.