How to Make It
Preheat the oven to 325°. In a pie plate, toss the garlic cloves with the olive oil. Cover with foil and roast for about 50 minutes, or until the cloves are soft and golden. Let cool, then peel the garlic; reserve the oil.
In a large bowl, combine the water with the yeast, 1/4 cup of the flour and 2 tablespoons of the garlic oil. Let stand until frothy, about 30 minutes. Using a large spatula, fold in the remaining 4 1/4 cups of flour, the roasted garlic and the kosher salt until a wet dough forms; be very careful not to smash the garlic.
Cover the bowl with plastic wrap and let the dough rise until doubled in bulk, about 1 1/2 hours. Gently punch down the dough, scraping it up from the bottom of the bowl. Cover the dough and let it rise again until it is nearly doubled in bulk, about 1 hour.
Preheat the oven to 500° for 30 minutes with a pizza stone set on the bottom shelf. Alternatively, generously oil a large baking sheet. Turn the dough out onto a lightly floured surface, flatten it slightly and divide it into quarters. Roll or stretch each piece into a 1/2-inch-thick round and transfer the rounds to 2 floured rimless cookie sheets. Let the dough rounds rise for 30 minutes.
Prick the dough rounds all over with a fork. Brush with some of the garlic oil and sprinkle with sea salt. Slide 2 of the rounds directly onto the pizza stone or onto the oiled baking sheet and bake for 10 to 12 minutes, or until golden and crisp. Repeat with the 2 remaining rounds. Cut the flat breads into wedges and serve with any remaining garlic oil.