How to Make It
In a small saucepan, combine the olive oil, shallot, rosemary and garlic and cook over low heat until fragrant, about 10 minutes. Let cool completely, then season with salt and pepper.
Very lightly grease a small baking sheet with the garlic-rosemary oil. In a small bowl, whisk the warm water with the yeast and sugar. Let stand until foamy, about 5 minutes. Whisk 2 teaspoons of the garlic-rosemary oil into the yeast mixture.
In a food processor, pulse the flour with the salt. With the machine on, drizzle in the yeast mixture until the dough just starts to come together. Scrape the dough onto a work surface and knead until smooth. Cut the dough into 4 pieces and formthem into balls, then transfer them to the prepared baking sheet. Brush lightly with the garlic-rosemary oil. Cover with a damp kitchen towel and let stand in a warm spot until nearly doubled in size, about 1 hour.
Meanwhile, preheat the oven to 500° and set a pizza stone on the lowest rack. On a lightly floured work surface, roll two of the dough balls out to 11-by-5-inch ovals and transfer to a lightly floured pizza peel. Lightly brush the dough with the garlic-rosemary oil and slide the breads onto the hot stone. Bake for about 3 minutes, until lightly golden and just risen. Transfer the breads to a towel to keep warm. Repeat with the remaining dough. Serve the flatbreads with the remaining garlic-rosemary oil. make ahead The flatbreads can be kept at room temperature for up to 3 hours.