In a small bowl, combine the warm water and sugar. Sprinkle the yeast over the top and let it sit for about 5-10 minutes until it becomes frothy.
In a large mixing bowl, combine the warm milk, yogurt, olive oil, and the activated yeast mixture. Stir until well blended.
In another bowl, whisk together the all-purpose flour, baking powder, and salt. Gradually add this mixture to the wet ingredients, stirring until a dough begins to form.
Transfer the dough to a lightly floured surface and knead for about 5-7 minutes until it becomes smooth and elastic.
Place the kneaded dough in a lightly oiled bowl, cover it with a damp kitchen towel, and let it rise in a warm place for about 1-2 hours, or until it has doubled in size.
Once the dough has risen, punch it down and divide it into equal portions (about 8 pieces). Roll each piece into a ball and then flatten it with a rolling pin into an oval or circle, about ¼ inch thick.
Heat a cast iron skillet or tawa over medium-high heat. Once hot, place the rolled naan onto the skillet. Cook for about 1-2 minutes until bubbles form on the surface, then flip and cook for another 1-2 minutes on the other side.
Once cooked, remove the naan from the skillet and brush it generously with melted butter. Sprinkle with freshly chopped parsley for a pop of color and flavor.