Make the dough: Combine the flour, baking powder, salt, and sugar in the bowl of a stand mixer fitted with the dough hook. In a medium bowl, whisk the yogurt, egg and add 1-1/2 cups of lukewarm water and the oil. Mix. Pour the yogurt mixture into the flour mixture and mix on low speed until a soft, sticky dough starts to clump around the hook, about 5 minutes. If the dough seems too wet, add more flour, 1 tsp. at a time.
Line a baking sheet with parchment and dust lightly with flour. Turn the dough out onto a lightly floured surface and divide it into 10 equal pieces. Form each piece into a ball and arrange them on the baking sheet. Lightly brush the dough with oil, cover with plastic, and let sit 1 hour before shaping.
Make the chutney: Place all the chutney ingredients in a food processor and pulse until uniformly granular.
On a lightly floured surface, roll a dough ball into a 5-inch circle. Spread 1 T of the chutney in the center, leaving a 1/2-inch border. Sprinkle 1 tablespoon of cheese over the chutney. Gather the borders to form a pouch (see picture) pinching it to seal in the filling. Turn the pouch pinched side down and, using very light pressure, roll it into a 6-inch circle. Transfer to a parchment-lined baking sheet. Layer rolled out naan with parchment until ready to grill.
Prepare a medium charcoal or gas grill fire and wipe grates with a lightly oiled paper towel. Grill the breads in batches pinched side down, covered, until they puff up and the undersides brown lightly in places, 2 to 3 minutes. Turn over and cook the other side, covered, until grill marks form and the breads are cooked through, 2 to 3 minutes. Just before taking them off the grill, turn the breads pinched side down and brush lightly with butter or olive oil. Serve warm.
These are best, right off the grill but leftovers can be refrigerated and saved for another time. Just place them in a toaster or warm oven before serving.