Add 2¼ teaspoons active dry yeast, 1 cup warm water (110°F), ¼ cup granulated sugar, ¼ cup milk, 1 egg, 2 teaspoons salt, 2 tablespoons olive oil, and 4¼ cups all-purpose flour to the bread machine. Add the wet ingredients first, followed by the dry ingredients. Do not add the garlic yet.
Set the bread machine to the dough cycle and allow it to complete the first rise.
When dough has completed first rise in the bread machine, remove and knead 2 teaspoons minced garlic into the dough until evenly distributed.
Pull off pieces of dough about the size of a golf ball. Roll into balls and place on a cookie sheet. Cover with a damp towel and allow to rise until doubled in volume, about 30 minutes.
Preheat grill to high heat (around 375 degrees).
Once the second rise is complete, brush the grill with melted butter.
Roll one ball of dough out into a thin circle. Place dough on grill and cook for 2 to 3 minutes until fluffy and showing brown bubbled areas.
Brush the top side with butter and flip. Brush browned side with butter and cook until browned another 2 to 4 minutes.
Remove from heat and continue until all the naan has been cooked.