Combine warm water, sugar, and yeast in a large bowl and let stand until foamy, about 5 minutes.

Whisk in the yogurt and oil until smooth. Add flour and salt; mix with a sturdy spoon until a shaggy dough forms.

Turn the dough onto a lightly floured surface and knead until smooth and elastic, 3–4 minutes; it should feel slightly tacky but not stick to your hands.

Lightly oil the bowl, place the dough inside, cover, and let rise in a warm spot until nearly doubled, about 45 minutes.

Punch down the dough, divide into 8 equal pieces, roll each into a ball, and flatten to ovals about ¼-inch thick.

Heat a cast-iron or heavy non-stick skillet over medium-high. Lightly brush the hot skillet with oil. Cook one naan at a time until bubbles form and the underside is deeply golden, 1–2 minutes; flip and cook 1 minute more, adjusting heat to avoid burning.

Place the naan on a plate and cover with a towel to keep warm. When ready to serve, brush with melted butter and serve warm.