In a small bowl, combine the sugar, warm water, and yeast. Stir well. Let the mixture sit for about 10 minutes, until the yeast becomes foamy and activated.
Transfer the all-purpose flour to a flat surface and create a well in the center. Pour in the yeast mixture, salt, yogurt, and oil, then knead the dough until the surface is smooth and shiny, about 10 minutes.
Cover the dough with a damp cloth and let it rise in a warm place, such as beside the stovetop or in a warm oven. The dough should double in size in about 1 hour.
Divide the dough into 8 equal portions. Roll each portion into an 8-inch circle using a rolling pin. Sprinkle and press some minced garlic and chopped cilantro leaves onto the top surface of the dough.
Heat a cast-iron skillet over high heat and lightly grease the surface with some oil. Place the dough in the skillet with the garlic and cilantro side facing up. When the naan puffs up and bubbles and burnt spots appear, flip it over to cook the other side. Repeat the process until all the dough is cooked.
Brush the naan with melted butter and serve warm.