Slice the peaches and remove the pit. Then, in a bowl, toss with brown sugar and balsamic vinegar (not the glaze). Set aside.
Season pork chops with a few drizzles of olive oil, garlic powder, Italian seasoning, Kosher salt (about ½ teaspoon per pork chop), and ground black pepper.
In a skillet, add a few drizzles of olive oil over medium heat. Once the skillet is hot, cook the pork chops about 5 minutes per side. See notes for internal temperatures. Transfer to a plate and set aside.
Wipe the skillet clean. Then, melt 2 tablespoon of the butter and then add the peaches. Sauté until slightly caramelized. Then, add the chicken broth along with the thyme and rosemary sprigs. Simmer over low heat for a few minutes until the sauce is caramelized slightly thickened. Season with salt and pepper to taste.
Turn off the heat. Then, immediately add the remaining 1 tablespoon of butter and stir until melted. This will help thicken the sauce and make it glossy. Note: It's important to add the butter after the heat is off, otherwise it will liquify and not thicken the sauce.
Return the seared pork chops to the pan, and spoon some of the sauce and peaches over. To serve, drizzle with balsamic glaze (not vinegar) on top.