Wicked Easy Piadine

Of course, being from California I see those and think tortillas. After looking at your recipe I see it is very similar to a Rick Bayless tortilla recipe.

On YouTube is an episode of Rick Bayless in his show One Plate at a Time making homemade flour tortillas.
The episode is called "Making Quesadillas". A search on YouTube for Rick Bayless Flour Tortillas will find the episode.

I made these recipe notes while watching that episode: 

Rick Bayless Homemade Flour Tortillas

Makes One Dozen, 7-inch, flour tortillas

3/4 cup (175 gr) cold tap Water
1 tsp (6 gr) Table Salt
2 3/4 cups (3/4 lb) (340 gr) All Purpose Flour
1/3 cup (65 gr) Shortening (vegetable or pork fat)

Mix salt into the cup of water.
Place flour and shortening in food processor.
Pulse until shortening is well mixed.
With food processor running, pour in salty water slowly.
Process until dough forms a ball. It should be slightly sticky.
Remove from food processor and roll dough out into sausage shape on slightly floured counter.
Cut into 6 even size pieces.
Cut each of the 6 pieces in half to make 12 pieces of dough.
Roll each piece of dough into a ball.
Place 12 dough balls on plate and cover with plastic wrap.
Let dough balls rest on plate, covered with plastic wrap on counter, for 1/2 hour.
Roll out each dough ball into a 7-inch tortilla, one at a time as you cook them. Dust counter with a little flour
while rolling out tortilla. Using a rolling pin, roll out tortilla from the center to edge, while rotating tortilla.
Cook in a dry or slightly oiled cast iron skillet over medium heat.
Turn over after a minute or two.
Cook until tops of bubbles that form are browned.
As each tortilla is cooked, stack in a cloth lined (clean dish towel, etc) basket and cover with the cloth.
They will steam and soften each other as they sit in the covered basket while you cook the remaining tortillas.

Makes 12 flour tortillas.

Source: One Plate at a Time with Rick Bayless, episode "Making Quesadillas", as viewed on YouTube.