In the bowl of a large food processor fitted with a dough blade or a large bowl, sprinkle yeast over warm water. Let sit until foamy, about 5 minutes.
In a medium bowl, mix together the flours and 1 teaspoon salt. Slowly incorporate the flour into the foamy yeast until dough comes together. If too wet, add more flour. If too crumbly, add more warm water. Knead the dough until soft and elastic. The dough should easily pull away from the sides of the bowl. If using a food processor, remove dough and place in large, lightly oiled bowl. Cover and let rise until doubled, about 1 hour.
In a large pan, drizzle olive oil over medium heat. Add onions and cook until softened and translucent, about 5 minutes. Add tomatoes and increase heat to medium high. Cook, stirring often, until most of liquid has evaporated. Remove pan from heat and let cool.
Preheat oven to 325 degrees F and lightly grease a 15 inch long baking sheet.
On a lightly floured surface, roll dough to fit size of pan. Transfer to prepared baking sheet, cover, and let rise until puffy, about 15 minutes.
Evenly spread cooked onions and tomatoes over the risen dough. Sprinkle with remaining salt, black pepper, and oregano. Bake in preheated oven until golden and onions begin to caramelize, about 1 hour. Let sit for 5 minutes before slicing and serving.