In a large bowl, dissolve yeast in warm water. Let stand about 10 minutes, until frothy. Stir in sugar, milk, egg, salt and about 3 cups of flour to make a soft dough.
Knead on a lightly floured surface until smooth.
Place dough in a greased bowl & cover with a damp cloth until doubled in size.
Punch down dough and knead in garlic. Pinch off small handfuls of dough about the size of a golf ball. Roll into balls and place on a tray.
Cover with a towel and let rise until doubled in size, about 30 minutes.
At grill side, stretch out each ball of dough into a thin circle by dipping fingers in melted butter.
Place dough on the grill on medium heat; cook 2 to 3 minutes, or until puffy and browned.
Brush cooked side with butter, turn dough over and cook until browned, another 2 to 4 minutes.