Preheat oven to 400˚F.
Pat dry pork chops with paper towels.
Using a sharp paring knife, cut a 2-inch deep pocket on the side of each pork chop. DO Not cut through. You just want to make a pocket for the stuffing. Set aside.
In a small bowl combine cheese, pesto, and garlic.
Stuff the pork chops with the pesto filling and secure with toothpicks. Set aside.
In a small bowl combine oregano, rosemary, thyme, pepper, and salt; rub both sides of the pork chops with the spice mix.
Heat 2 tablespoons vegetable oil in a large oven-safe skillet; add pork chops to the heated skillet and cook for 3 minutes per side, or until browned. (Sear the pork chops two at a time for easier turning.)
Remove pork chops from skillet and set aside; keep covered.
Add remaining oil to the skillet and set over medium-high heat.
Add sliced onions to the hot oil and cook for 4 minutes, or until softened, stirring frequently.
Carefully add the chicken broth; stir and scrape up all the browned bits from the bottom of the pan.
Add pork chops back to the skillet.
Transfer skillet to the oven and continue to cook for 10 to 12 more minutes, or until internal temperature of the pork chops reaches 145˚F. Try not to overcook the pork chops because if you do, they will be tough and dry.
Remove from oven and let stand 5 minutes.
Remove toothpicks and serve.