Dissolve yeast in warm water in a large mixing bowl; let stand 5 minutes. Add flour and 3/4 teaspoon of salt to yeast mixture; stir with a a mixer equipped with dough hooks or use a wooden spoon until smooth. Turn dough out onto a lightly floured surface; knead a few minutes, until flour is fully incorporated. Shape dough into a ball; spray inside of a bowl with cooking spray and place the dough ball inside it. Seal bowl with plastic wrap and allow to rest at room temperature for an hour.
Heat a pan on medium with 1 tablespoon of olive oil. Saute the onions in the pan for a few minutes, until the onions become translucent. Allow to cool somewhat before proceeding to next step.
Combine onion, parsley, remaining olive oil, paprika, cumin, 1/2 teaspoon of salt, and crushed red pepper. Mix thoroughly into a paste.
Cut dough into 8 equal portions. Start with one portion and cover remaining dough with a wet kitchen towel to prevent drying. Flatten each portion until very thin and shape into a square. Spoon 1 tablespoon onion mixture in center of dough. Fold left and right sides of dough together until they meet in the middle. Fold top and bottom sides together in the same way, wetting the dough if needed to get the flaps to stick. Repeat for remaining dough portions and onion mixture.
Heat 1/2 teaspoon oil in a large nonstick skillet over medium heat. Add 4 flatbreads to pan; cook for 2 minutes on each side or until crisp and golden. Transfer flatbreads to cooling rack. Repeat procedure with remaining 1/2 teaspoon oil and 4 flatbreads. Serve immediately.