People often find this pie to be one of my most exotic and inventive, but when I think back on the way I developed it, that's not how it seems to me at all. There was the asparagus in front of me, and I wanted to make it work for a pizza; shaving it was the answer, so it would be thin and yield to quick cooking. That looked a lot like a bird's nest to me, hence the quail eggs--and then there's the cheese, of course, pulling everything together.
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Cut away about 2 inches of the base of each asparagus spear. With a vegetable peeler, shave the entire asparagus from bottom to top, reversing your grip and rotating as necessary to shave as much as possible. Don't rush it; be deliberate for the greatest precision. You should have about 90 grams (3 ounces) of very thin ribbons.
With the dough on the peel, sprinkle the Parmigiano evenly over the surface and distribute the chunks of Saint Nectaire on top. Arrange the asparagus shavings over the cheese.
With quick, jerking motions, slide the pie onto the stone. Broil for 21/2 minutes under gas. The cheese should be bubbling, the crust only slightly charred.
Using the peel, pull the pizza out of the oven. Close the oven to conserve heat.
Crack the eggs very carefully to keep each yolk whole. Place the eggs around the pizza (one for each slice). Sprinkle the salt evenly over the pie. Return to the oven to broil for 1 minute, until the eggs are set but not hard and the charring is deeper.
Using the peel, transfer the pizza to a tray or serving platter. Slice into wedges (cutting through the egg yolks to allow them to spread slightly). Serve immediately.
Shaping the Disk (Method 2):
Take one ball of the dough and generously flour it, your hands, and the work surface. Then press it down and gently stretch it out to 6 to 8 inches. Supporting the disk with your knuckles toward the outer edge and lifting it above the work surface, keep stretching the dough by rotating it with your knuckles, gently pulling it wider and wider until the disk reaches 10 to 12 inches. Set the disk on a well-floured peel. It is now ready to be topped.
Cover the bowl with plastic wrap or a kitchen towel and allow it to rise at room temperature (about 72 degrees F) for 18 hours or until it has more than doubled. It will take longer in a chilly room and less time in a very warm one.
Flour a work surface and scrape out the dough. Divide it into 4 equal parts and shape them: For each portion, start with the right side of the dough and pull it toward the center; then do the same with the left, then the top, then the bottom. (The order doesn't actually matter; what you want is four folds.) Shape each portion into a round and turn seam side down. Mold the dough into a neat circular mound. The mounds should not be sticky; if they are, dust with more flour.
Note: If you don't intend to use the dough right away, wrap the balls individually in plastic and refrigerate for up to 3 days. Return to room temperature by leaving them out on the counter, covered in a damp cloth, for 2 to 3 hours before needed. Don't freeze the dough, but you can store it in the refrigerator, wrapped in plastic, for up to three days. In effect, when you're set to use it, you have your own ready-made dough.
Yield: Makes 4 balls of dough, enough for 4 pizzas
Cook's Notes: While I'm not picky about the flour--either bread flour or all-purpose is fine--what does concern me is how the dough is handled. Treat it gently so the dough holds its character, its texture. When you get around to shaping the disk for a pie, go easy as you stretch it to allow it to retain a bit of bumpiness (I think of it as blistering), so not all of the gas is smashed out of the fermented dough. I prefer to hold off on shaping the ball until just before topping it. If it's going to sit for a while--more than a couple of minutes--cover it with a damp kitchen towel to prevent it from drying out. I offer you two approaches for shaping. The simpler one, executed completely on the work surface, is slower than the second, where you lift the disk in the air and stretch it by rotating it on your knuckles. Lifting it into the air to shape it is more fun, too.