In a large bowl, sprinkle the 1 (.25 ounce) package active dry yeast into 1 cup warm water. Stir gently and let stand about 10 minutes, until foamy.
Add 1/4 cup white sugar, 3 tablespoons milk, the beaten egg, and 2 teaspoons salt to the yeast mixture. Stir to combine.
Gradually add 4 1/2 cups bread flour to the bowl, stirring until a soft dough forms.
Turn the dough onto a lightly floured surface and knead for 6 to 8 minutes, until smooth and elastic.
Lightly oil a clean bowl, place the kneaded dough in the bowl, turn to coat with oil, cover with a damp cloth, and let rise in a warm place about 1 hour, or until doubled in volume.
Punch down the dough and, if using, knead in 2 teaspoons minced garlic until evenly distributed.
Divide the dough into small handfuls about the size of a golf ball. Roll each piece into a smooth ball and place them on a tray, spaced so they do not touch.
Cover the tray with a towel and let the dough balls rise about 30 minutes, or until roughly doubled in size.
During the second rise, preheat the grill to high heat and lightly oil the grill grates.
Working one dough ball at a time at the grill, roll a ball into a thin circle.
Place the rolled dough on the hot, oiled grill and cook 2 to 3 minutes, until the side on the grill is puffy and lightly browned.
Brush the top (uncooked side) with the 1/4 cup melted butter, flip the naan, brush the other side with melted butter, and cook another 2 to 4 minutes, until browned and cooked through.
Remove the cooked naan from the grill and repeat steps 10–12 with the remaining dough balls.