In a large mixing bowl, combine the active sourdough starter, flour, milk, yogurt, and salt. Mix until a shaggy dough forms.
If the dough feels too dry, add a small splash of milk or water at a time just until it comes together. The dough should be soft but still slightly firm, not sticky or wet.
Knead for 5 to 7 minutes, or until smooth and elastic.
Place the dough into a bowl, cover, and let it rest at room temperature for about 6 hours, or until puffy and roughly doubled in size. Rise time will depend on room temperature and starter strength.
Turn the dough out onto a lightly floured surface and divide it into 6 to 8 equal pieces.
Shape each piece into a ball, then roll each one into an oval or circle about ¼ inch thick.
Heat a cast iron skillet or heavy pan over medium-high heat.
Place one rolled piece of dough into the hot skillet. Cook for 1 to 2 minutes, or until bubbles form and the bottom has golden brown spots.
Flip and cook the second side for another 1 to 2 minutes, or until cooked through and golden in spots.
Repeat with the remaining dough.
Brush the warm naan with melted butter and sprinkle with parsley or cilantro. Serve warm.