In a large bowl, stir together the warm water, sugar, and yeast. Let sit 5–10 minutes until foamy.
In a separate large bowl, whisk together the flour and salt. Make a well in the center and add the egg and Greek yogurt.
Pour in the yeast mixture and olive oil. Mix until a shaggy dough forms, then knead a few minutes until smooth.
Place the dough in a lightly oiled bowl, cover, and let rise in a warm place until doubled, about 1 hour.
Divide the dough into 8 equal balls. Place on an oiled baking sheet, cover, and rest 20–30 minutes.
Roll each ball out on a floured surface to about ⅛ inch thick.
Preheat the Blackstone to medium-high (375–400°F) and spread a thin layer of oil over the surface.
Cook the naan 2–3 minutes per side, until puffed and golden with blistered spots. Repeat with remaining dough.
For the garlic butter, stir together the melted butter, garlic, and parsley. Brush over the warm naan and serve.