In a large bowl, stir together yeast and 1 3⁄4 cups water heated to 115° let sit until foamy, about 10 minutes. In a large bowl, whisk together flour, semolina, whole wheat and barley flours, salt, coriander, caraway, mahlepi (if using), and pepper until combined. Add yeast mixture and stir to form a dough. Transfer dough to a floured work surface and knead until smooth, about 5 minutes. Shape dough into a ball and place in a lightly oiled bowl; cover bowl with plastic wrap and let sit until doubled in size, about 1 hour.
Meanwhile, make the tomato sauce: Heat 3 tablespoons olive oil in a 4-qt. saucepan over medium-high heat. Add onions; cook until soft, about 10 minutes. Add tomato paste; cook, stirring, until glossy, about 2 minutes. Add marsala or port, honey, cinnamon, chile flakes, and tomatoes; bring to a boil. Reduce heat to low and cook, partially covered and stirring occasionally, until sauce thickens, 30–40 minutes. Season sauce with kosher salt and set aside.
Heat remaining oil in a 12" skillet over medium heat. Add zucchini and season with salt and pepper. Cook, stirring, until tender, about 8 minutes; set aside.
Uncover dough, divide into 8 equal pieces, then roll each into a ball. Transfer dough balls to a floured baking sheet and cover with a damp tea towel; let rest for 30 minutes. Working with one dough ball at a time, transfer dough to a lightly floured work surface and use a rolling pin to roll dough into an 8" disk about 1⁄4" thick; transfer the disk to a parchment paper-lined, floured baking sheet, sprinkle with more flour, and repeat with remaining dough, placing a piece of parchment paper between each rolled disk. Cover disks with plastic wrap until ready to use.
Heat a 12" cast-iron skillet over medium-high heat. Working with one dough disk at a time, brush with olive oil and place in skillet. Cook, flipping once, until puffed and golden brown, 3-4 minutes. Spoon tomato sauce or zucchini over top and sprinkle with feta and more chile flakes.