Melt 1 Tbsp. butter in a heavy pan over medium-high heat. Cook the onions over low heat until soft, 5 minutes. Transfer to a bowl an cool to room temperature
Melt the remaining butter and pour into a large mixing bowl. Add the water, onions, salt, and flour 1/2 cup at a time. Work the dough into a ball. If the dough continues to be sticky, add additional flour 1 tsp. at a time.
Turn the dough onto a floured surface and work until slightly firm. Divide into 8 pieces, rolling each into a ball. Let rest 3 minutes.
Roll each ball into an 8" round. Cover with a damp towel while rolling the rest.
Heat an ungreased pan over high heat. When a drop of water vaporizes immediately when dropped in the pan, place the first round in the center. Brown for 3-4 minutes per side. Cool on a rack.
This doesn't appear to be a very 'authentic' naan recipe. For one, naan are supposed to be leavened (even artificially), which this is not. Additionally, naan are only cooked in the pan on one side, and should then be finished on the other side by exposure to direct heat. This recipe is more in line with roti.
Didn't actually measure the onion to 1 cup, but it seemed like an appropriate amount once cooked. The dough was rather sticky, even after adding an additional 1/4 cup, probably because of the extra onion. Using a 12" cast-iron pan, was able to cook two oblong naans at a time. They taste pretty good, but do get a bit chewy if stored airtight.
Made a double batch, but still only made 8 roti. This time they are a much better size. I cooked them in a large cast iron pan, and misted them with water and covered with a lid when first stretching the dough in the pan, then misted and left uncovered when flipping. Again, these are delicious, but this time they are large enough.