In a mixer combine yeast, sugar, milk, and warm water. Let sit for a few minutes until bubbly.
Add egg, flour, and salt and mix until no dry spots remain. The dough should be a little sticky, but manageable enough to roll without making a mess– add more flour if needed and knead for about 8 minutes.
Turn dough out of mixer bowl and divide into golf ball-sized balls. Let rest for a minute.
Roll dough balls into thin, oblong pieces. The thinner you can get it, the better; they will puff up quite a bit on the grill.
Heat grill to medium-high.
Combine butter with minced garlic, if using, and brush one side of the dough rounds with it. Place the rounds butter-side down on the grill and cook for 2-3 minutes. Brush the uncooked side with butter and flip, cooking for and additional 2-4 minutes or until there are visible grill marks and bread is puffed.
Brush with more butter, if desired, and serve warm.