To make the dough, in a bowl, stir together the yeast, water and 2 tablespoons of the flour. Let stand until foamy, about 5 minutes. Add 3 cups of flour, the oil, and salt, and stir with a heavy wooden spoon to make a dough. Turn out onto a lightly floured surface and knead until smooth, adding more flour as needed to make a soft but still slightly moist dough. Shape into a ball, flatten slightly, dust with flour and cover with clean kitchen towel to rise until nearly doubled in size, about 45 minutes.
Punch the dough down, knead, and cut into 6 equal pieces. Roll out each 1 to a circle about 1/4-inch thick, 6 to 8 inches in diameter.
Heat a griddle or cast iron pan (or grill) over high heat. Prick the dough with a fork and cook on the griddle until golden, 2 to 3 minutes per side. Remove, brush lightly with the extra-virgin olive oil and repeat with the remaining dough.
To serve, pile the toppings of choice into the center of each warm grilled round. Roll the bread around the toppings of choice and serve immediately.
Bresaola and Arugula:
Divide the arugula leaves, bresaola, and Parmesan among piadine rounds. Top with a sprinkling of pepper and drizzle with balsamic vinegar.
Onion and Gorgonzola:
Divide the spinach, onions, and cheese among piadine rounds. Top with a sprinkling of walnuts and drizzle lightly with oil.