Stir together the sugar, water and yeast and let sit until yeast is foamy, 5 to 10 minutes.

Place the flours in a large shallow bowl and make a well in the center. Add the yeast mixture to the center of the well along with the yogurt, salt, and oil. Using your hands, mix the wet ingredients into the flour little by little until the mixture is thoroughly combined. Turn the dough out onto a clean lightly floured work surface and knead until the dough is smooth, supple, and elastic, 5 to 10 minutes. Transfer the dough to a clean bowl or cutting board, cover with a damp kitchen towel, and set aside in a warm place until the dough has doubled in size, about 1 hour. Using a sharp kitchen knife, cut the dough into 8 equal sized pieces.

Heat a grill to high heat. Combine the melted butter with the garlic in a small saucepan over medium heat and cook until the garlic is fragrant, 2 to 3 minutes. Set the melted butter and garlic mixture close to the grill.

Working with one or two pieces of dough at a time, fold the cut edges of the dough under to form a rough ball shape. Place the dough balls onto a lightly floured surface. Using a lightly floured rolling pin, roll each ball into a thin circle about 8- or 10-inches in diameter. The dough is very forgiving and need not be perfectly circular – a rustic shape adds to the appeal of the flatbreads. Brush one side of the dough with the butter, then place on the hot grill, buttered side down, close the grill lid, and cook until the dough is puffed with deep golden grill marks on the bottom, usually 1 ½ to 2 minutes. Brush the top of the dough with some of the melted garlic butter, then quickly turn the dough over, close the grill lid, and continue to cook until the bread is puffed in places and has golden brown spots on the second side, 1 ½ to 2 minutes longer. This goes very quickly – it can be helpful to have another person rolling and prepping the dough for you as you cook the flatbreads.

As the flatbreads come off of the grill, brush them with a bit more melted garlic butter and sprinkle with the fresh herbs. Stack the flatbreads in a towel-lined basket to keep warm until ready to serve.