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Place the warm water in the bowl of a stand mixer fitted with the dough hook. Sprinkle the yeast over the top and let it sit for 10 minutes.
Add the flours, salt and olive oil to the yeast mixture, and knead on medium-low (speed 2 on a Kitchen Aid) until the dough comes together, then knead for another 10 minutes. You should have a somewhat firm dough (firmer than for a usual pizza crust) that gathers around the dough hook.
Scrape the dough into a lightly oiled bowl, cover with plastic wrap, and let rise until doubled in volume, about 1 to 1 1/2 hours.
An hour before you're ready to bake, remove all but the bottom rack of your oven, place a baking stone on the rack, and crank the oven up to 500ºF.
Heat the oil in a wide skillet over medium heat. Add the spring onions and green garlic and a big pinch of salt, and saute until tender, 10 minutes or so. Remove from the heat and set aside.
Meanwhile, bring a large saucepan full of water to a boil. Prepare an ice bath and set aside. Shove the spinach into the boiling water and cook for about 1 minute, until bright green and tender. Drain the spinach and plunge it into the ice bath for a minute or two, then squeeze the all the water out of it - it will look like a tiny, green lump. Place the lump on a cutting board, and give it a rough chop.
In a medium bowl, combine the sauteed onions and garlic with the spinach. Add the cheeses, marjoram and salt, tasting and adding more salt if you think it needs it. Divide the filling into 6 equal portions.
Cut two sheets of parchment paper into 6 rectangles measuring roughly 8x6" and set aside.
Turn the risen calzone dough out onto a lightly floured surface and gently press to deflate. Use a metal bench scraper or chef's knife to cut the dough into 6 equal pieces (my dough weighed 16 ounces, so each ball weighed about 2 1/2 ounces, but you can just eyeball it if you prefer). Round each piece of dough into a rough ball. Set them to the side and cover with plastic wrap to rest for 10 - 20 minutes, but no longer (this will make the dough easier to roll out).
Remove 1 ball of dough and place on a lightly floured surface. With a rolling pin, roll into an 6-7" circle. The dough will be springy, so you will have to roll and stretch it a bit to make it cooperate.
Place 1 portion of the filling on the lower half of the dough circle, and spread it evenly on the bottom half, leaving a 1" boarder around the bottom (see photo, above). Fold the top half of the dough over the filling, leaving 1/2" of the bottom part of the dough sticking out. Use your fingertips to press around the silhouette of the filling, sticking the top portion of dough to the bottom part of the dough. Now fold up the 1/2" of the bottom part of the dough up onto the top, pleating it with your fingertips, pressing very firmly to make it stick together. Place the calzone on a piece of parchment paper, and trim away the excess parchment, leaving a 1" boarder.
Repeat with two more dough balls. Cut three 2" slits in the top layer of each calzone. Brush the calzone all over the top and sides with olive oil, and sprinkle each with a pinch or two of salt.
Place the calzone on their papers on the pizza peel, and slip them onto the heated stone in the oven. Bake until golden and the filling is bubbling, about 12 - 15 minutes, then use a pair of tongs to pull them out, still on their papers, back onto the pizza peel. Let cool for at least a few minutes before serving. (If letting them cool longer, set them on a cooling rack; this will prevent the bottoms from steaming and going soggy.)
While the first three calzone are baking, assemble, then bake, the remaining three.
The baked and cooled calzone will keep in the fridge for up to a few days; reheat in theoven or toaster oven at 350º for 5-10 minutes until hot and crispy.