Heat the olive oil in a large, wide skillet.
Sprinkle the salt and pepper on both sides of the pork chops and lay them in the pan. Cook for 3 to 4 minutes on each side or until nicely brown.
Add the onions, garlic, mushrooms, and seasonings all around the pork.
Add the broth and bring to a simmer. Turn the heat down to medium-low, cover, and gently simmer for 30 minutes.
Pour the half-and-half into a small bowl and whisk in the Dijon mustard.
Push the pork and mushrooms to the side of the pan, so the liquid accumulates in the center.
Turn the heat down to low and drizzle the half-and-half/mustard mixture into the center of the pan, stirring to combine.
Arrange all the ingredients evenly around the pan again and sprinkle in a little fresh parsley, if desired.
Let this cook over low heat for about five more minutes, just to heat it through and allow the flavors to blend.
Taste and adjust the salt and pepper to your liking before serving.
