Add the sliced onions to the Dutch oven and sprinkle with 1 teaspoon kosher salt. Stir to coat the onions in the butter and oil, then cook over medium to medium-low heat, stirring every few minutes, until the onions are soft, deep golden, and caramelized, about 25–30 minutes. Adjust the heat if they start to brown too quickly; you want slow, even color.
Stir in the minced garlic and thyme and cook for about 1 minute, just until fragrant.
Pour in the beef broth and Worcestershire sauce (if using), scraping up any browned bits from the bottom of the pot with a wooden spoon. Let this mixture simmer for 3–5 minutes to slightly reduce and concentrate the flavor. Turn off the heat.
Taste the onion mixture and add a pinch more salt or pepper if needed. This is your 1 savory onion topping, so make sure it tastes good and balanced.
Using a large spoon or ladle, carefully transfer most of the onion mixture to a bowl, leaving just a thin layer of onions and broth in the bottom of the Dutch oven to keep the pork from sticking.
In a separate skillet, heat the remaining 1 tablespoon olive oil over medium-high heat. Sear the seasoned pork chops for 2–3 minutes per side, just until lightly browned. You are not cooking them through, only giving them some color. (If you prefer, you can sear them directly in the Dutch oven before making the onions, then remove and proceed with the onions in the same pot.)
Arrange the raw, seared pork chops in a single layer in the bottom of the Dutch oven over the thin layer of onions and broth.
Using your ladle, spoon the reserved savory onion topping evenly over the raw pork chops, making sure each chop is well covered with caramelized onions and some of the broth. This close-up moment of ladling is exactly what you’d want to capture in a homey kitchen photo.
Cover the Dutch oven with its lid and place it over medium-low heat on the stovetop. Cook gently for 20–25 minutes, or until the pork chops are cooked through and reach an internal temperature of 145°F (63°C). You can also bake, covered, in a 350°F (175°C) oven for the same amount of time if you prefer.
Once the pork is cooked, remove the lid and sprinkle the shredded Gruyere cheese evenly over the onions and pork chops. If using Parmesan, scatter it over the top as well.
Cover the Dutch oven again and let it sit over low heat for 3–5 minutes, just until the cheese is melted and gooey. If you’d like a browned, bubbly top and your Dutch oven is oven-safe, you can place it under the broiler for 2–3 minutes, watching closely.
Remove from the heat. Let the pork chops rest in the Dutch oven for about 5 minutes so the juices settle. Sprinkle with chopped fresh parsley if you like, then serve each pork chop generously topped with the cheesy, savory onion mixture and some of the broth from the bottom of the pot.
