In a large bowl, combine sourdough starter, milk, melted butter, yogurt (or sour cream), honey, and salt until smooth.
Stir in whole wheat flour, then gradually add all-purpose flour until a soft, slightly tacky dough forms. You may not need to add all the flour. Dough should be supple, not stiff.
Cover with plastic wrap or a damp towel and rest 20–30 minutes (fermentolyse).
Over the next 90 minutes, perform 3–4 rounds of stretch & folds, wetting hands and surface lightly. Stop when dough is smooth, elastic, and cohesive.
Transfer to a greased bowl, cover, and bulk ferment for a few hours until it rises 30–50%.
Divide dough into 8–10 balls and rest 20–30 minutes, covered, to relax gluten.
On a lightly floured surface, roll or stretch each ball into an oval or teardrop, ⅛–¼ inch thick. Avoid over-flouring so the naan can bubble.
Heat a dry cast-iron skillet over medium-high until very hot. Cook each naan 45–60 seconds on the first side, until bubbles form.
Flip and cook 30–45 seconds more, aiming for nice charred spots without burning.
Brush hot naan with melted butter or ghee, stack, and cover with a towel to keep soft. Serve hot or warm.