For the Piadina Dough
4 ½ cups cake flour (plus more for dusting)
1 tablespoon baking soda
1 teaspoon salt
2/3 cup lard or vegetable shortening (cut into tablespoons)
1 cup ice water
For the Gravy
1 pound spicy Italian sausage (out of the casing)
2 tablespoons flour
1 ½ cups milk
1 teaspoon salt
Pinch freshly grated nutmeg
4 slices prosciutto (cut into thin ribbons)
For the Piadina Dough:
Combine the flour, baking soda, and salt in a food processor and pulse to mix. Scatter the pieces of lard over the flour and pulse just until incorporated. With the food processor running, add the water and process just until the dough begins to clump together.
Turn the dough out onto a floured surface and roll to ¼-inch to ½-inch thick. Heat griddle to medium heat. Cut the dough into 3-inch pieces. Working in batches, place the rounds on the griddle and cook until light golden brown on the first side, about 1 to 2 minutes. Turn and repeat on the other side.
For the Gravy:
In a sauté pan over medium heat, slowly cook the sausage, allowing the sausage to render all of its fat. Cook, crumbling with a wooden spoon, until sausage is crisp and dark brown, about 20 minutes.
Warm milk in a small sauce pot. Add the flour, and using a wooden spoon, stir vigorously. Slowly add the milk, stirring continuously to prevent clumping and stir in the prosciutto. Bring sauce to a boil and cook until sauce has thickened and reduced slightly, and then remove from heat. Season with salt and nutmeg. Serve the gravy over the Piadina.