For the chops: Heat a heavy-bottomed skillet over medium heat. Season the pork chops with salt and pepper. Set aside.
Mix together the milk and eggs in a shallow dish. Place a heaping 1/2 cup of flour onto a plate, add a pinch of salt and pepper and mix through. Add the panko to another plate and season with a pinch of salt and pepper.
Bread the pork by dredging each chop first in the seasoned flour, shaking off the excess. Next, transfer to the egg/milk mixture, coating both sides. Then, cover with the seasoned panko. Set aside.
Add the oil and 3 tablespoons of the butter to the skillet. Add the breaded chops and cook until golden and crisp, 2 to 2 1/2 minutes per side. Remove to paper towel-lined plate.
Without cleaning the skillet, carefully add the capers and remaining 3 tablespoons butter, allowing the butter to melt. Sprinkle the remaining 2 tablespoons of flour over the melted butter and cook, stirring, for 30 seconds. Add the wine and stock and bring to a boil. Simmer until the sauce begins to thicken, about 2 minutes. Add 1 tablespoon of the lemon juice (or more to taste) and adjust the seasoning.
For serving: Place the arugula on a platter and drizzle with the lemon juice. Shingle the pork chops on top. Drizzle the sauce over the pork chops and finish with the shaved Parmesan and parsley. Serve with the remaining lemon wedges and any extra sauce on the side.