In the same pan, heat 1 tablespoon of butter over medium heat.
Add in sliced onions and add a pinch of salt. Cook while stirring occasionally, until soft and caramelized, about 10 minutes. (Add in 1 tablespoon of the chicken broth if the pan becomes too dry.)
Add the garlic and thyme; cook until fragrant, about 30 seconds.
Add 2 tablespoons of the remaining flour to the pan. Mix the flour into the onions and cook to dissolve, about 2 minutes.
Pour in the chicken broth, scraping up the browned bits from the bottom of the pan. Let the liquid reduce and thicken slightly, about 2 minutes.
Whisk in the buttermilk (or cream) and simmer for 1-2 minutes until thick and creamy.
Return the pork chops to the pan. Coat them in the sauce and let simmer until the pork is completely cooked through, about 5 minutes (or until the pork is cooked to your desired doneness). (The sauce will continue to thicken due the coating on the pork. If too thick, add a little cream or broth to thin out until reaching your desired consistency.)
Taste test and season with salt and pepper, if needed. Garnish with the chopped parsley before serving. Serve warm.