Combine the flour, baking soda, and 1 teaspoon of salt in the bowl of an upright mixer, fitted with a dough hook attachment. Add the butter and mix on low speed until incorporated, about 2 minutes. With the machine running, slowly add the water until the mixture forms a dough around the hook. Transfer the dough to a lightly floured work surface and knead for 5 minutes until smooth. Cut the dough into 4 equal pieces Form into disc shapes and wrap in plastic wrap. Refrigerate for 30 minutes.Place a grill pan over medium-high heat or preheat a gas or charcoal grill. On a lightly floured work surface, roll out each piece of dough into an 8 to 10-inch circle, about 1/8-inch thick. Brush each circle with the extra virgin olive oil and grill for 4 minutes each side. Remove the piadina from the grill to cool slightly. Combine the ricotta cheese and lemon zest in a small bowl. Season with salt and pepper. Spread each piadina with 1/2 cup of the ricotta mixture. Sprinkle the Fontina cheese evenly over the ricotta cheese. Arrange the prosciutto slices on top of the cheeses.
Cut each piadina into 8 wedges and transfer to a serving platter. Garnish with the chopped basil.