Instructions

1. Arrange a rack in the middle of the oven and heat the oven to 425°F. Tear 4 ounces French or Italian bread into large pieces and place in a blender or food processor fitted with the blade attachment. Pulse into coarse breadcrumbs, then measure out 2 cups (save any remaining for another use).
2. Finely chop 2 medium scallions and 1 garlic clove. Pick the leaves from 7 fresh thyme sprigs until you have 2 teaspoons, then coarsely chop. Pick the leaves from 8 fresh parsley sprigs and coarsely chop until you have 2 tablespoons. Grate 2 ounces Monterey Jack cheese on the large holes of a box grater (about 1/2 cup). Finely grate 1 ounce Parmesan cheese on the small holes of the grater (about 1/4 cup).
3. Melt 2 tablespoons of the unsalted butter in a medium skillet over medium heat. Add the breadcrumbs and season with 1/4 teaspoon of the kosher salt and 1/4 teaspoon of the black pepper. Cook, stirring often, until toasted and lightly browned, about 3 minutes. Add the scallions, garlic, and thyme, and cook until the scallions are softened, about 1 minute.
4. Add 1/2 cup of the low-sodium chicken broth. Cook, stirring occasionally, until the broth is absorbed, about 30 seconds. Transfer to a medium bowl and let cool slightly. Add the parsley, Monterey Jack, and Parmesan, and stir to combine.
5. Working with one pork chop at a time, place one hand flat on top of the pork chop with the bone side facing away from you. Use a thin, sharp knife (such as a boning knife) to cut a large pocket in the pork chop, going all the way to the bone.
6. Evenly and firmly fill the pockets with the stuffing. Press the top of the chops with your palm to flatten for even browning, but do not let the stuffing come to the edge (it will naturally push out a little as the chops cook). Season the chops all over with the remaining 3/4 teaspoon kosher salt and 1/2 teaspoon black pepper.
7. Heat 1 tablespoon of the olive oil in a large skillet over medium-high heat until very hot but not smoking. Add 2 of the pork chops and cook until well browned, 3 to 4 minutes per side (they will not be cooked through). Transfer to a rimmed baking sheet. Add the remaining 1 tablespoon olive oil to the pan and repeat browning the remaining 2 pork chops and transferring to the baking sheet.
8. Place the baking sheet in the oven and roast until the pork chops are just cooked through, 5 to 15 minutes. Let rest for 5 minutes. Meanwhile, do not clean the skillet but remove any bits of stuffing. Make the pan sauce.
9. Return the skillet to medium heat. Carefully pour in 1/4 cup dry white wine. Simmer, scraping up any browned bits from the bottom of the pan, and cook until syrupy, about 1 minute. Add the remaining 3/4 cup chicken broth and simmer until reduced by two-thirds (to about 1/3 cup), 3 to 4 minutes.
10. Remove the skillet from the heat. Add the remaining 1 tablespoon unsalted butter and swirl the skillet until the butter is fully melted and combined. Taste and season with kosher salt and black pepper as needed. Serve the sauce over the chops.