To make the garlic-rosemary oil, in a small saucepan, combine the oil, garlic, shallot, and rosemary, and heat over low heat for about
10 minutes, or until fragrant. Remove the saucepan from the heat and season the oil to taste with salt and pepper.
To prepare the flatbread dough, in a small bowl, stir the warm water, yeast, and sugar to blend. Set aside for about 5 minutes, or until foamy.
In a food processor, combine the flour and salt, and process to blend. With the machine running, add the yeast mixture and 1 tablespoon of the garlic oil and process just until the dough comes together. Transfer the dough to a work surface and knead until smooth and elastic.
Divide the dough into 8 pieces (about 3 ounces each) and shape into balls. Place the dough balls on an oiled baking sheet and rub them lightly with some of the garlic oil. Cover with a piece of oiled plastic wrap and let rise in a warm, draft-free spot for about 45 minutes, or until doubled in size.
To shape and grill the flatbreads, prepare a grill for medium-high heat. Lightly oil the grill grates.
Using a rolling pin, roll each dough ball out on a floured work surface into a thin 11x5-inch oval (the shape does not have to be perfect). Set them aside on the oiled baking sheet.
Working in batches, brush the flatbreads with some of the garlic oil and lay them on the grill grate. Grill for about 2 minutes per side, or until grill marks form and the bread is cooked through. Wrap the breads in a clean kitchen towel to keep them warm. (Make-Ahead: The flatbreads can be made up to 1 day ahead and stored airtight at room temperature. To reheat, wrap them in foil and warm in a 350°F oven.)
To serve, brush the flatbreads with more of the garlic oil, if desired, and serve with any remaining oil for dipping.
For Baked Flatbreads:
Position a rack in the lower third of the oven and set a pizza stone on the rack. Preheat the oven to 500°F. Working with one piece of dough at a time, roll the dough out as directed above. Lightly brush the top of the flatbreads with garlic oil and drape the flatbreads, oiled side down, over the stone. Bake for about 5 minutes, or until golden brown on the bottom and baked through. Wrap the breads in a clean kitchen towel to keep them warm and serve as above.