Heat oven to 375°F. Melt butter in skillet; soften onion and celery 5 minutes. Add broth, sage, and 1/4 teaspoon salt; simmer and fold into bread cubes.
With small knife, cut deep side pockets in chops, keeping other edges intact. Loosely fill with warm stuffing; secure with wooden toothpicks. Season pork with remaining salt and pepper.
Heat oil in large oven-safe skillet; brown chops 2 minutes per side in two batches if needed. Return all in one layer or transfer to baking dish.
Bake 20 to 30 minutes until stuffing center reaches 165°F and pork at least 145°F. Check both in thickest chop.
Rest at least 3 minutes; remove every toothpick. Spoon hot pan juices beside chops to serve.