Start with the naan dough. In a large bowl, stir together the water, yeast and sugar and let stand for 5 minutes, until foamy. If it doesn’t foam, the yeast is inactive; replace it with a fresh jar of yeast.
Stir in the flour, salt, canola oil, yogurt and egg, and stir until the dough comes together, then knead for a few minutes, until it’s soft, smooth and elastic. Cover with a tea towel and let rise until doubled in size; about an hour.
Meanwhile, heat a drizzle of oil in a large, heavy skillet set over medium-high heat. Cook the chicken for 7–8 minutes, until opaque and starting to brown. Add the butter chicken sauce and cilantro and simmer for 15–20 minutes, until the chicken is cooked through and the sauce has thickened. Let cool as you wait for dough to finish rising. It's even better if it gets a chance to chill completely in the fridge.
Divide the dough into six pieces. On a lightly floured surface, roll out each piece into an 8-inch circle or oval. Pile a spoonful of butter chicken onto each circle, top with a bit of grated cheese and fold over, pinching the edges (you may have to fold the edge up over itself) to seal. Transfer to a parchmentlined baking sheet and cut a few slits on the top of each with a sharp knife. Preheat the oven to 400?F.
Bake for 20 minutes, until bubbly and golden.