In a large mixing bowl, combine the dry ingredients: the all-purpose flour and baking powder. Mix them well to ensure even distribution.
Gradually pour in the room temperature water (or water-milk mixture) while continuously stirring the mixture. This helps to gradually incorporate the liquid into the dry ingredients.
Add the olive oil (or lard) to the mixture and start kneading the dough. Knead until you achieve a uniform and smooth dough. This should take around 5-7 minutes. You can knead by hand or using a standing mixer,
Form the kneaded dough into a ball shape and cover it. Allow it to rest for 30 minutes. This resting period helps relax the gluten and makes the dough easier to work with.
After the resting time, divide the dough into six equal portions. This will make slightly thicker piadina that are about 6 to 8 inches in diameter OR thinner ones that are 10 inches in diameter. Shape each portion into a small ball and then cover them with a clean kitchen towel. Let them rest for another 15 minutes. This second resting period further improves the dough's texture and elasticity.
Alternatively, you can divide the dough into 12 pieces to make smaller, thinner piadina (About 6 to 8 inches).
On a floured countertop, take one of the rested dough balls and gently flatten it into a round shape. Flour each side well and begin to roll each one out into a flat, round shape. Aim for a diameter of approximately 6 to 8 inches (or up to 10 inches for a thinner version). Rub extra flour, as needed, onto the rolling pin as you roll out each piadina and constantly turn as you roll. (see Notes for tips on rolling a uniform circular shape).
Heat a skillet or a flat pan over medium-high heat. Once it's hot, carefully place the rolled-out dough onto the pan. Cook for 1 to 3 minutes on each side or until the piadina turns golden and develops light brown spots. Check after one minute to gauge the heat/cooking. Poke large bubbles with a fork.
As each piadina is cooked, remove it from the pan and stack it on a plate. You can place a clean kitchen towel on them to keep them warm and soft.
Serve the freshly cooked piadine warm, with your choice of fillings and toppings.