Preheat oven to 375 degrees.
Combine the Flour, Yeast, and Salt in a bowl; pour 1 1/3 cups Warm Water into a measuring cup and stir in the Olive Oil; Mix the liquid with the dry ingredient to make a soft but firm dough, adding more liquid as needed, and either turn this out onto a surface and knead by hand or keep in bowl and use a mixer fitted with a dough hook and knead until smooth, supple and full of elastic life; form into a ball, wash out and dry bowl, Oil it, and turn the dough in it so it’s lightly oiled all over; Cover with plastic wrap and leave to rise for an hour or so or until doubled in size.
Trim the tops off the Garlic heads, making sure they remain whole, sit them in some torn-off squares of foil, dribble over some oil and wrap them loosely; the packages should be baggy but the foil tightly sealed at the edges; cook for 45 minutes; they should not be mushy by this stage but still just holding their shape; remove from oven, unwrap and let cool; Turn oven up to 400 degrees.
Tear the parsley leaves from their stems and add a good handful to the bowl of the food processor and chop; Squeeze the soft garlic cloves out of their skins and into the bowl and process again; pour in enough extra-virgin olive oil to make a runny paste down the funnel, while still processing, and leave this pungent emulsion where it is while you get back to the bread.
When the dough has risen, punch it down and leave to rest for 10 minutes; divide the dough in half and get out 2 sheets of baking parchment. Sit a ball of dough on each, and roll out to form a curved rectangle or bulky oval; then, using your hands, press out a little more; transfer the breads on their papers to the baking sheets, cover with tea towels and leave to rise and get puffy for about 25 minutes.
Poke your fingers all over the tops of the breads to dimple them, and then go back to the food processor and pulse once or twice to make sure the Parsley, Garlic and Oil are combined and pour this green mixture all over the corrugated flatbreads.
Put the baking sheets into the oven and bake for 20 minutes or until the breads are cooked – becoming golden in parts, with the garlic flecks a darker brown and the rims puffing up around the oily topping.
Whip out of the oven and drizzle over a generous amount of good extra-virgin olive oil; sprinkle some salt and set down on the table for people to tear greedily at with their bare hands.