Combine yeast, sugar, and water in a glass measuring cup; let sit for 10 minutes.
Mix flour, baking soda, and baking powder in a large bowl.
Whisk yeast mixture with yogurt and milk, then stir into dry ingredients.
Knead dough until smooth and soft, place in an oiled bowl, cover with plastic wrap, and let rise for 2 hours.
Turn dough onto a floured surface, knead briefly, and divide into 12 portions.
Roll each portion into a 1/4-inch-thick oval.
Heat cast-iron skillet over moderately high heat, press minced garlic into the dough, brush with melted butter, and cook each naan for about 1 minute until puffy.
Flip, cover, and cook for another minute; brush with butter, sprinkle with salt, and keep warm in a towel-lined bowl.