Using your fingertips, mix atta, sooji, ajwain, and salt in a medium bowl, then add ghee and mix until well incorporated. Mix in water, adding more water 1 tablespoon at a time to form a firm dough; knead to form a ball. Cover dough and let rest for 30 minutes.
Line a large baking sheet with paper towels. Heat 2 inches of oil in a large wok or pot to 350°F over medium-high. Divide dough into 12 golf-ball-sized balls, rolling each into a smooth ball. Coat balls with a thin layer of oil and roll out on a work surface into 5-inch disks about 1/8-inch thick.
Working with 1 disk at a time, carefully add dough to hot oil in wok. Use a slotted spoon to gently press poori under oil on 1 side until it puffs up, then press down on other side until poori has completely puffed and is golden brown, 1 1/2 to 2 minutes. Flip poori over and cook until golden, about 30 seconds. Transfer poori to prepared baking sheet. Repeat with remaining dough and serve immediately.