For the grilled pork chops: Whisk together the olive oil, mustard, apple juice, parsley, lemon zest and juice, salt, pepper and garlic in a medium bowl.
Put the pork chops in a baking dish or resealable gallon-sized bag. Pour the marinade over the meat. Marinate for at least 1 hour at room temperature and up to 8 hours refrigerated.
For the apple-mango chutney: Meanwhile, heat a medium saucepan over medium-high heat. Add the olive oil and heat until hot and shimmering. Add the onion and cook until softened, 2 to 3 minutes. Add the mango, apple juice, lemon peel and juice, sugar, cumin, apples and cinnamon stick. Cook over medium heat, stirring often and allowing the mixture to bubble and reduce, 15 to 20 minutes. Remove the lemon peel and cinnamon stick before serving. The chutney can be stored in an airtight container for up to a week.
Preheat an indoor grill pan to medium heat.
Grill the pork chops until an instant-read thermometer inserted into the thickest part of the chops registers 145 degrees F, 4 to 5 minutes per side. Let the meat rest for 5 minutes before serving. Garnish with the chutney and chopped parsley.