Preheat the oven to 400 degrees F (200 degrees C) with oven rack in center position.

Cook bacon in a nonstick skillet over medium heat until almost crisp, about 5 minutes. Add onion and poblano pepper; cook until onion turns translucent, 5 to 6 minutes. Add peach; cook until tender and starting to render some juice. Transfer to a bowl.

Stir saltines, thyme, black pepper, salt, and cayenne pepper into peach mixture; add 2 tablespoons chicken broth to moisten as needed. Refrigerate until ready to use.

Cut a pocket in center of each pork chop, starting with a small incision on fat side of chops, exactly halfway down, using the tip of a knife to cut as close to the edges as possible without poking through. Try to make pocket incisions at least 2 inches wide.

Fill pockets with peach stuffing, packing and pressing in firmly. Season both sides of chops with salt.

Heat olive oil in an oven-safe skillet over high heat. Add chops; sear until browned on one side, about 3 minutes. Carefully flip chops and transfer skillet to the oven.

Bake in the preheated oven until an instant-read thermometer inserted into centers reads 145 degrees F to 150 degrees F (63 to 66 degrees C), about 15 minutes.

Transfer chops to a plate; cover loosely with foil.

Return the skillet to the stovetop; place a towel over the hot handle. Add ¼ cup chicken broth and balsamic vinegar; bring to a boil while scraping the browned bits of food off the bottom of the skillet with a wooden spoon. Off heat, stir in butter. Adjust seasoning if desired; serve over pork chops.