Add the flour, sourdough starter, milk, Greek yogurt, olive oil, and salt to a bowl. Mix thoroughly with your hands until everything is evenly combined.
Cover the bowl and let the dough rise for +/- 8 hours, or until it doubles in size.
Punch the dough down, then divide it into 8 equal pieces on a clean surface (about 100g each).
Heat a cast-iron skillet over medium/high heat. Working with one ball of dough at a time, roll each piece into a circle, around ⅛” thick. Place the rolled dough in the hot skillet and cook for 1-2 minutes on each side. There will be noticeable brown spots on each side.
On a separate burner, melt the butter in a small skillet. Add the garlic and parsley. Sauté for 2 minutes, just until the garlic is fragrant.
Remove the naan from the skillet and brush with melted butter. Serve warm, or allow to fully cool and store in an airtight container.