To make the dough: Weigh your flour; or measure it by gently spooning it into a cup, then sweeping off any excess. In a medium bowl or container, combine the flour, yeast, sugar, and salt; then add the water. Stir to combine into a rough but cohesive dough.  , Cover the bowl and allow the dough to rest at room temperature for 30 minutes. , Uncover the dough and complete a bowl fold: Use wet hands to grab a section of dough from one side, lift it up, then press it down into the middle. Give the bowl a quarter turn (90°) and repeat this 4 to 6 times.  , Cover the bowl and allow the dough to rise at room temperature for at least 12 hours and up to 24 hours.    , An hour before planning to bake, generously flour a work surface. After its long rest, the dough will appear bubbly and be very sticky. Use a bowl scraper to divide the dough in half (about 200g per piece). Transfer both pieces of dough to the well-floured surface.  , To preshape the dough: Working with one piece at a time, stretch the outside edge of the dough slightly away from its center, then fold back to its center, pressing gently to seal. Repeat this process 5 or 6 times, working your way around the dough to create a round ball. Repeat with the other piece of dough, then place both dough balls seam-side down on the floured work surface. , Cover and allow the dough to rise for 45 to 60 minutes. , While the dough is rising, place a rack in the upper third of the oven, or at least 8" below the broiler. Place a baking steel or stone on the rack and preheat the oven to 500°F. Make sure your oven is at the required temperature for at least 30 minutes before baking so the steel or stone can preheat fully.  , Lightly flour a baker’s peel or the back of a baking sheet.  Cut a 9" parchment round in half to create two half-moons. (Alternatively, cut 9" half-moons from a sheet of parchment.) Dust the half-moons lightly with flour and place them on the floured peel or baking sheet., Once risen, the dough balls will be puffy and marshmallow-y. Working with one piece at a time, use floured fingertips to gently depress the dough from the center outwards, being careful not to deflate the outer edge of the crust. This is important — leaving an untouched 1/2" to 1" border around the edge at this stage will result in a beautiful bubbly outer rim once baked.  , Lift the dough from the work surface and use your knuckles to gently stretch the dough into a 9" to 10" circle. If the dough is at all sticky, gently sprinkle more flour on the dough and your hands. Use two hands at once to gently move the dough in a circle, allowing gravity to perform the stretch. If you find your dough is resistant, set it down on the floured surface for 5 to 10 minutes to allow the gluten to relax.  , Brush the surface of both rounds of dough with a thin layer of olive oil, avoiding the borders. Fold each round in half to make a semi-circle.  , Transfer the folded dough pieces onto the parchment half-moons on the peel or baking sheet. Jiggle the uncooked dough back and forth to ensure it slides easily and isn’t sticking., Transfer the dough, along with the parchment, onto the preheated baking stone or steel. Bake for 4 to 5 minutes, or until the dough sets and becomes light brown in spots.  , Turn on the oven’s top broiler and continue baking for 2 to 3 minutes, or until golden brown and charred in spots. Keep a close eye at this stage and carefully rotate the dough if needed to prevent burning on the top.   , Once baked, transfer the dough pockets to a wire rack to cool slightly before filling, about 2 minutes, or until you can handle them safely.  , To assemble: Gently open the dough pockets, being careful of the steam. Start by tearing open the burrata (one ball per sandwich) and evenly distributing it onto the bottom half of each piece of dough. (If using mozzarella or ricotta, distribute the cheese evenly between each piece of dough.) Layer on the mortadella, folding and rolling the individual slices so the ruffled edges face outward. Zest the lemon over the mortadella to taste, then squeeze a bit of lemon juice directly on top. Sprinkle with pistachios, then grate Parmesan cheese over the top. Finish with nutmeg, pepper flakes, and sea salt before drizzling with olive oil.  , To garnish: Fold the mortadella pizza sandwiches in half, closing the pockets; brush each with more olive oil. Sprinkle more pistachios and Parmesan on top.  
, Storage information: Mortadella pizza sandwiches are best enjoyed fresh from the oven. Baked, unfilled dough can be stored, covered, in the refrigerator for up to 3 days. To reheat, wrap in aluminum foil and place directly onto an oven rack in a 300°F oven for 5 to 10 minutes or until warm.