Sprinkle yeast over warm water in a mixing bowl and allow to stand until the yeast forms a creamy foam, about 5 minutes. Mix in 2 cups of flour, salt, and shortening; beat for 2 minutes with a fork. Stir in as much of the remaining 1 1/2 cup flour as needed.
Turn dough out onto a floured surface and knead until smooth and elastic, kneading in more flour if dough is sticky. Form into a ball, cover with a kitchen towel, and let rest in a warm area for 15 minutes.
Preheat oven to 500 degrees F (260 degrees C).
Divide dough into 12 equal portions; flour your hands and roll each piece into a ball. Cover dough balls with a kitchen towel and let rest for 10 minutes. Flatten the balls into rounds on a floured surface, cover with kitchen towel, and let rest 10 more minutes. Gently roll each dough ball into a circle about 6 inches in diameter on a floured surface. Place pita breads in a single layer on ungreased baking sheets.
Bake in preheated oven until the pita breads puff up, 3 to 4 minutes. Flip breads over with a spatula, return to oven, and bake 2 more minutes. Let cool on wire racks before cutting pita breads in half and gently separating tops and bottoms to form pockets for filling.