In a large bowl, combine flours and salt with your fingers or a whisk. Make a well in the center and pour in warm water, sugar, and yeast. Let sit for 10 minutes, until foamy, then add oil to liquid and mix together with your hands or spoon until a craggy ball forms. Knead it together, gathering any loose flour, into a ball, then transfer to a counter and knead for 8 to 10 minutes, until a smooth, elastic ball has formed. Oil your now-empty bowl and return dough to it, and cover the bowl with plastic wrap. Let rise for 1 1/2 to 2 hours; it should double.

Pour water, sugar, and yeast into the bottom of the mixer’s bowl and let stand for 10 minutes. Add oil to yeast mixture, then flours, then salt and use the machine’s dough hook to pull the mixture into a craggy ball. Knead on low for 5 minutes, scraping down as needed, until a smooth, elastic ball has formed. Briefly remove it from your mixer bowl, oil the bowl, and return the dough to it, covering the bowl with plastic wrap. Let rise for 1 1/2 to 2 hours; it should double.

Heat 2 tablespoons olive oil in the bottom of a medium-sized pot over medium, then add garlic, cook until it barely picks up color, and add pepper flakes and oregano, stir again. Add canned tomatoes (be careful — it’s going to splash up) and salt and stir to combine. Add basil, bring the mixture to a simmer, then reduce to a low simmer, for 10 minutes, stirring occasionally. Remove and discard basil. Adjust seasonings to taste. Set aside to cool to lukewarm or room temperature while dough rises.

Mix cheeses together in a large bowl and refrigerate until needed.

Heat oven to 400 degrees F. Line a large baking sheet with parchment paper. On a floured surface, roll your dough into the thinnest rectangle that you can, pulling and stretching it as needed. You’re looking for 1/16-inch thickness; the longer sides should be parallel to you. Spread about half of the tomato sauce over the whole rectangle in a thin, but not too thin, layer. Season with salt and pepper. Sprinkle with about half the cheese, scatter with slices of pepperoni and slivers of basil, if using. Fold the left and right sides of the dough over the filling to meet at the center. Spread the top with more sauce, seasonings, cheese, and toppings. Fold the top and bottom in so they meet in the center; spread the top with more sauce, seasonings, and remaining cheese and toppings. Fold top half over bottom half, take a deep breath, and lift this from the counter and onto the parchment-lined baking sheet. Prick the top all over with a fork.

Bake for about 1 hour, until deeply browned all over and charred in some spots. Rotate the pan as needed for even coloring. Let stand at room temperature for 10 minutes before cutting into squares with a serrated knife, and serving.

Heat oven to 400 degrees F. Line a loaf pan with a sling of parchment paper. On a floured surface, roll your dough into the thinnest rectangle that you can, pulling and stretching it as needed. You’re looking for 1/16-inch thickness; the longer sides should be parallel to you. Spread tomato sauce over the middle three-fifths of the rectangle in a thin, but not too thin, layer. Season with salt and pepper. Sprinkle with about 2/3 to 3/4 of the cheese, scatter with slices of pepperoni and slivers of basil, if using. Fold the two plain sides of the dough over so their edges overlap in the middle of the rectangle by 2 inches. Spread the left two-thirds of the dough with more sauce, seasonings, and the remaining cheese and toppings. Fold the righthand, plain third, halfway over the sauce. Fold the lefthand side of the dough over the righthand, as if completing the tri-fold of a letter. Fold the dough crosswise over itself and gently twist the ends of the rope together once. Take a deep breath, and lift this from the counter and into the parchment-lined loaf pan. Prick the top all over with a fork.

Bake for about 1 hour, until deeply browned all over and charred in some spots. Rotate the pan as needed for even coloring. Immediately invert the pie onto a rack, remove the loaf pan and parchment paper, and let the pie cool in this position for 10 minutes. Invert the pie right-side-up before slicing with a serrated knife to serve.

Reheat fantastically. Wrap them in foil in a 350 degree oven until warmed through, about 15 minutes.