Heat 1 tbsp olive oil in a large skillet over medium heat. Add the sausage and cook for 4 to 5 minutes, breaking it up with a spoon, until browned and cooked through.

Add the apple, onion, celery, sage, salt, and pepper. Sauté for 4 to 5 minutes, stirring occasionally, until the apple has softened and the onion is translucent.

Stir in the panko and apple cider. Cook for 1 to 2 more minutes, until the breadcrumbs absorb the liquid and the mixture holds together when pressed. Taste and adjust seasoning if needed. Set aside and let cool slightly.

If any chops have a thick white fat cap on the edge, trim and discard it. A fat cap won't render during a quick sear and stays rubbery. If the fat is thin and already mostly trimmed, you can leave it.

Cut a deep horizontal pocket in the thickest side of each chop with a sharp boning or paring knife, stopping about 1/2 inch from the opposite side and edges. You want the pocket to be as wide as possible without cutting through.

Season both the outside and the inside of each pocket generously with the 2 tsp kosher salt and 3/4 tsp black pepper.

Spoon the stuffing into each pocket and use your fingers to press it in firmly and compactly. Secure the open edge with one or two toothpicks to keep it closed during searing. A little overflow at the opening is fine.

Preheat the oven to 400°F (200°C).

Heat 1 tbsp olive oil in a large oven-safe skillet over medium-high heat until shimmering. Add the stuffed chops and sear for 2 minutes without moving them, until a deep golden crust forms on the bottom.

Use tongs to flip each chop, squeezing the open side gently shut as you turn it to prevent stuffing from falling into the oil. Sear for another 2 minutes on the second side.

If all four chops don't fit in one skillet without crowding, sear them in two batches, then transfer them to a rimmed baking sheet for the roasting step.

Transfer the skillet (or baking sheet) to the oven. Roast for 10 to 15 minutes, until an instant-read thermometer inserted into the thickest part of the pork (not the stuffing) reads 140 to 145°F.

Transfer the chops to a plate and let them rest for 5 minutes before serving. Do not cut in early or the juices will run out.

Place the same skillet over medium heat. Add the chicken broth and apple cider. Use a wooden spoon to scrape up all the browned bits from the bottom of the pan. Let it simmer for 2 to 3 minutes until slightly reduced.

Stir in the Dijon mustard and balsamic vinegar if using. Let the sauce reduce for another minute, then remove from heat and whisk in the butter one piece at a time until the sauce is glossy and slightly thickened.

Pour in any juices that have accumulated on the plate from the resting chops. Season with a small pinch of salt and pepper to taste. The broth reduces and concentrates as it simmers, so taste before adding salt.

Remove the toothpicks from each chop. Press any stuffing that fell out back into the pocket. Spoon the pan sauce generously over each chop and serve right away.