Preheat the oven to 400°.
Peel most of the paper off the head of garlic and trim the top so the cloves are just exposed. Drizzle olive oil over the head and wrap in foil.
Roast garlic at 400° for 40 minutes, until center is tender. You can continue roasting in 10-minute intervals until golden and caramelized.
While the garlic is roasting, combine yeast, sugar, and water in a mixing bowl.
Let sit five minutes until the yeast is foaming, then whisk in oil, yogurt, and egg.
Stir in salt and two cups of flour.
Turn the dough onto a lightly floured surface and knead, slowly adding remaining flour.
Smash the roasted garlic cloves into a paste and work into the dough. The final dough should be smooth and soft, not sticky.
Loosely cover the bowl with a damp towel and let rise in a warm place until doubled, about an hour.
After rising, cut the dough and shape into eight small balls.
Heat a heavy-bottomed skillet over medium heat. Roll one ball out to a quarter-inch thickness.
Cook dough until golden brown on the bottom and large bubbles are forming on the top, then flip and cook the other side to golden brown.
Roll out and repeat with each ball of dough individually to get the most bubbles.
You can optionally brush each piece of naan with melted butter as it comes out of the skillet. You should totally do this.