kosher salt and freshly-ground black pepper, to taste
Preheat the oven to 400° F. Line a rimmed baking sheet with parchment paper or lightly-grease with olive oil. Set aside.
Season both sides of the pork chops with the garlic powder, sage, and rosemary. Season generously with salt and pepper, to taste.
Melt 2 Tbsp of the butter in a large skillet over medium-high heat. Add the pork chops to the skillet, and sear until deep golden brown, about 2-3 minutes per side.
Transfer the pork chops to the prepared sheet pan. Add the green beans to the pan, in a single layer. Drizzle with olive oil, just enough to coat. Season with salt and pepper, to taste.
Bake for 7-10 minutes (depending on thickness), until the pork chops are golden and cooked through (reaching an internal temperature of 140° F), and the green beans are tender but still a bit crispy.
Meanwhile, wipe out the skillet with a paper towel, and return it to the burner. Melt the remaining 2 Tbsps of butter over medium heat. Add the brown sugar and cinnamon, and stir to combine.
Add the peaches, and cook, stirring occasionally, until the peaches are soft and fragrant, about 2-3 minutes. Turn the heat down to low, and continue to simmer, until the sauce thickens slightly, another 5 or so minutes more.
Remove the pork chops from the oven, transfer to a large plate (save any pan juices to drizzle over top!), and let rest for 5 minutes, tented loosely with aluminum foil. Top the baked pork chops with the peaches and sauce, and serve immediately, along with the green beans.