In a small bowl, stir together 1 teaspoon sugar, 1/2 cup warm water, and 1/4 oz (7 g) active dry yeast. Let sit about 10 minutes, until foamy.
Put 2 1/4 cups all-purpose flour and 1/2–1 teaspoon salt in a large bowl or on a work surface and mix. Make a well in the center.
Add the foamy yeast mixture, 1/2 cup plain Greek yogurt, and 1 tablespoon vegetable oil into the well. Stir or fold until a shaggy dough forms.
Turn the dough onto a lightly floured surface and knead until smooth and elastic, about 8–10 minutes.
Shape the dough into a ball, place it in a clean bowl, cover with a damp cloth, and let rise in a warm spot until doubled in size, about 1 hour.
After the dough has risen, punch it down and divide it into 8 equal portions. Using a rolling pin on a lightly floured surface, roll each portion into an 8-inch circle.
Sprinkle the top of each circle with the 3 cloves garlic, finely minced, and the 2 tablespoons cilantro leaves, chopped. Press the garlic and cilantro gently into the dough so they adhere.
Preheat a cast-iron skillet over medium-high heat. Lightly grease the skillet with a little oil.
Cook one naan at a time: place a rolled dough in the skillet with the garlic-and-cilantro side facing up. Cook until bubbles form and the underside has browned or charred spots, about 1–2 minutes. Flip and cook the other side until cooked through and lightly charred, about 30–60 seconds. Lightly grease the skillet as needed between naans.
Transfer cooked naan to a plate and brush both sides with the melted salted butter. Repeat with remaining dough and serve warm.