Combine the warm water, yeast, and 1 teaspoon of sugar in a cup or small bowl and set aside. In a large bowl, thoroughly mix the 2 cups of flour, baking powder, remaining 1 teaspoon of sugar, and salt then add the yeast mixture to it, along with the yogurt and oil and use a fork to bring it all together. The dough will be very sticky.
Use a bowl scraper to coax the dough out onto a well floured counter and knead it until soft and smooth, 3 to 5 minutes. Return the dough to the empty bowl, cover with a tea towel, and set aside at room temperature for 2 to 4 hours.
Scrape the dough out onto a floured counter and divide into six pieces. Roll each piece of dough in flour, pat it down with your hand, then use a rolling pin to evenly roll each one out into about a 7"-8" circle or tear drop shape.
Heat a heavy griddle or large frying pan on high until a few drops of water immediately sizzle and evaporate. Pick up one of the rolled-out naan, stretch it out a little if it has started to shrink, then lightly dampen one side of the dough by dipping your fingers in the bowl of water and spreading a little water on the dough. Using a sort of slapping motion, place that wet side of the dough down onto the hot pan and press it down with a spatula.
Fry the dough about a minute, (it will start to bubble slightly), then flip it over and fry the other side until charred, about 30 to 45 seconds.
Stack the naan on a plate as you take them from the frying pan, then brush one side of the finished breads with melted butter.
Serve naan warm or at room temperature. Store in a plastic bag in the refrigerate for 1 or 2 days, or double wrap and freeze for longer storage. Reheat in a microwave, oven, or skillet.