Preheat grill. Drizzle chops with oil and place on hot grill, just until marked on both sides, 2 minutes per side (do not burn). Transfer chops to indirect heat (cool side of grill) and lower lid, cooking slowly until internal temp of 140° is reached (transfer to a cast iron skillet on grill, if necessary, to slow cooking). Let rest 5 min before serving with Cola Barbecue Sauce and Sweet Potato Fries.
Cola Barbecue Sauce
In a sauce pot over medium-high heat, boil cola and brown sugar until syrupy and reduce to about ½ cup. Add remaining ingredients and bring to a gentle simmer, lowering heat to medium, cooking 8 min to combine flavors. Use immediately or chill in an airtight container. Sauce will keep up to one month refrigerated.
Sweet Potato Fries
Boil potatoes just until soft in center (easily pierced with pick). Drain and wedge potatoes into eighths. Toss with oil and mark on hot grill. Season with thyme, salt and pepper.