In a medium size bowl, add the sourdough discard, water, yogurt, sugar, and salt. Mix well with a fork (or dough whisk) to fully dissolve the sourdough starter and everything is mixed together.
Next, add 2 and ½ cups of the flour, and with a dough whisk or wooden spoon, mix in all the flour until it forms a rough ball. Using your hands, work the dough until it comes together to form a smooth ball. If the dough is sticky you can add the remaining ½ cup of flour as needed. Add 2 tablespoons at a time. The goal is to have a really soft dough that can still be handled.
Cover with a cloth and set aside for 4-5 hours or until it has slightly risen, but not necessarily doubled in size.
When ready to make, turn the dough onto a lightly floured surface and divide it into 8 pieces.
Using a lightly floured rolling pin, roll out the dough to a rough circle about ¼" thick. It should be thick enough that you cannot see the counter through the dough but not too thick where it takes a long time to cook.
Heat a cast-iron skillet or griddle over medium-low heat. Place the naan on the griddle and cook for about 2-3 minutes, or until it starts to turn golden brown.
Little bubble should start forming all over. That is exactly what should be happening.
Flip and cook the other side for an additional 2-3 minutes, or until it's cooked all the way through.
Transfer to a cooling rack and brush on melted butter.
Optional: Sprinkle with freshly chopped herbs.