For brining the pork chops: Combine the salt, sugar, peppercorns, bay leaves, garlic, lemon peels and parsley with 3 quarts water in a large pot or bowl and whisk together. Add the pork chops, cover and refrigerate for at least 24 hours, turning once halfway through. This may seem like a long time, but these are seriously big pork chops. Brining will make your pork so tender and flavor it throughout.
For the smashed potatoes: Place the potatoes in large pot and cover with salted cold water. The potatoes will soak up that salt like pasta and it will make a big difference in flavor. Cover and bring to a boil and cook until fork-tender, 20 to 30 minutes. Drain the potatoes, and return them to the same pot, allowing them to dry. Melt the butter with the half-and-half in a small saucepot over low heat. Add to the potatoes along with the cream cheese and season with salt and pepper. Smash with a potato masher and set aside, keeping warm until ready to serve.
For the mushroom escabeche: Heat the canola oil in a large saute pan over high heat. Add the mushrooms and saute until lightly browned in spots, 2 to 3 minutes. Season with salt and pepper, remove from the heat and reserve. Heat the olive oil in a small saucepot over medium heat and saute the garlic and shallots until softened, 2 to 3 minutes. Add the vinegar, sugar, chili flakes and lemon zest and juice. Bring to a simmer and then turn off the heat. Return the reserved mushrooms to the pot, toss to combine and absorb all of that flavor. Garnish with parsley.
For preparing the pork chops: Preheat the oven to 350 degrees F. Heat a grill pan over high heat. Remove the chops from the brine and dry completely with paper towels. Drizzle with canola oil and sprinkle liberally with salt and pepper. Place the chops on the grill and sear until browned, 5 to 6 minutes on each side. Transfer to a sheet tray and finish cooking in the oven until an internal temperature reaches 135 to 140 degrees F on an instant-read thermometer, 15 to 20 minutes. Transfer to a plate and tent with foil. Let rest 5 to 10 minutes.
Serve the pork chops over the smashed potatoes and top with the mushrooms.
Hon shimeji mushrooms, also known as brown beech mushrooms, can be found at Asian specialty markets or online. If hon shimeji are not available, you can substitute cremini or shiitake mushrooms.