Combine yeast, water, and sugar in a bowl and let the yeast bloom for about 10 minutes or so. Make a well with the flour and combine the yeast mixture, 2 tablespoons olive oil, and the yogurt into it, adding some more flour while kneading until the dough is no longer tacky.
Form the dough into a ball and lightly coat it with olive oil. Place it in a bowl, covered, in a warm place and let it rise until doubled for about an hour. Meanwhile, in a small saucepan, combine the half stick of butter and minced garlic and set it on very low heat on a back burner.
Punch the dough down and cut into tennis ball sized pieces. Dust a work surface with flour and roll the pieces out into rounds (it doesn't need to be perfect) until they're thicker than a tortilla, but thinner than a fluffy cooked pancake. I'm able to do 2 at a time.
Heat a tablespoon of olive oil in a cast iron skillet on medium and working in batches, fry the dough, flipping over when bubble form on one side, about 2 minutes or so each side. Remove to a plate. I'm able to fry one at a time. Replenish the olive oil a tablespoon at a time as you need it.
When all the naan is cooked, brush them with the butter garlic mixture on one side of each and serve.