Combine all of the ingredients for the marinade together, then coat each of the pork chops. Allow to marinate for at least two hours, up to overnight.
Season the chops with salt to taste, then grill over medium heat for six to seven minutes per side, or until 145° internal temperature. Allow the chops to rest for at least five minutes before serving.
To make the puree, steam the parsnips until tender.
Add the cooked parsnips with the rest of the ingredients to a blender and blend until very smooth and velvety.
Serve with the pork chops along with some sautéed greens.