In a large bowl, whisk together the yogurt, oil and egg.
Add the flour, baking powder and salt. Mix with a spatula until the dough starts to come together.
Knead the dough by hand for about 1 minute, until smooth and soft. It should be soft but not sticky.
Lightly flour your work surface. Roll the dough out into a rectangle, about 35 cm (14 inches) long. It doesn’t need to be perfectly shaped.
Cut the dough into 25 roughly equal squares using a knife or pizza cutter.
Line a large serving plate with a few sheets of paper towel and set aside.
Heat the sunflower oil in a large frying pan over medium heat. To check if it is hot enough, drop in a tiny piece of dough. If it starts sizzling immediately, the oil is ready.
Fry the dough in batches of 4–5 pieces, depending on the size of your pan. As soon as you add them to the oil, use a spoon to repeatedly scoop some of the hot oil over the tops of each piece. You will see the dough start to puff up like little pillows.
Fry for about 2 minutes, or until the bottoms are golden. Carefully flip them over and fry the other side for about 1 minute, checking as needed, until golden all over.
Transfer the fried pişi to the paper towel-lined plate to drain any excess oil.
Continue frying the remaining dough in batches in the same way. Serve warm.