For the dough, mix the yeast, ¾ cup warm water, and ½ cup flour together in a large bowl. When the mixture is foamy and active, add 4 more cups flour, the salt, olive oil, and remaining 1 cup water. Stir to mix, then knead until smooth, adding a little flour if necessary, but aiming for a soft dough. Cover and let rest for 2 hours, refrigerated, or overnight.
For the filling, in a large heavy skillet over high heat, wilt the onions quickly in 2 tablespoons olive oil and the butter, letting them color a bit but leaving them a little crunchy.
Add the cumin, coriander, red chile, paprika, and black pepper. Season well with salt. Taste and adjust the seasoning—the onions should be rather spicy. Remove the onions to a plate to cool, and sprinkle with the chopped parsley and cilantro.
Preheat the oven to 400°F. Divide the dough into six 5-ounce pieces. Knead each piece into a smooth ball. Cover with a clean towel and let the dough rest for 10 minutes.
To make the first pizza, roll out 2 dough balls into 8-inch rounds. Place one-third of the onion mixture on one of the rounds. Cover with the other round of dough. Pinch the edges together with your fingers. With the palm of your hand, press down on the package to flatten it, then roll out the filled dough to make a 12-inch circle (the onion mixture will spread inside the dough as you roll). Follow the same procedure to make 2 more pizzas.
Transfer one pizza to a lightly oiled baking sheet. Bake up to 2 pizzas at a time for 15 to 20 minutes, flipping the pizza halfway through the baking to ensure even browning. (The pizzas can be baked up to 2 hours in advance and reheated on baking sheets in a hot oven.) Paint the tops with a little olive oil and sprinkle with salt and cut into wedges just before serving.