Turkish fried dough absorbs oil when the oil is not hot enough; in cool oil, the dough cannot form a crust, so the oil soaks into it. A doughy center usually has the opposite cause: the oil is too hot, and the outside darkens before the inside cooks. Rolling the dough too thick or not letting it rise enough can also cause the same result. Keeping the oil at 170–180°C / 340–355°F lets the fried dough puff up and cook through.
This is a soft, yeasted dough; as soon as it enters the oil, two things should happen. The water on its surface should evaporate quickly and form a thin crust, while the air and steam inside make the dough puff up. At 170–180°C / 340–355°F, both happen: the fried dough rises to the surface within seconds, puffs up, and turns golden. If the oil is cool, the crust forms slowly; the dough sits in the oil during that time and absorbs oil through its pores. The result is a heavy, greasy, deflated piece of fried dough on the plate. Two pieces made from the same dough can turn out completely differently just because of the oil temperature.
Oil that is too hot causes the opposite problem. In very hot oil, the outside of the fried dough turns dark brown in one minute, but the heat does not have time to reach the center; when cut open, the middle is raw and doughy. So treat the first piece as a test: once it browns, cut it in half and check the inside, then adjust the heat if needed. You can judge the oil temperature with a thermometer or by watching the bubbles around the handle of a wooden spoon dipped into the oil; the bubbles should be active and steady, not foaming vigorously.
The dough itself also determines the result. Knead the dough until it comes together and no longer sticks to your hands, but do not make it stiff; stiff dough does not open up in the oil and stays dense inside. Let it finish rising: wait until it doubles in size. Underproofed dough will not puff up, while dough that overproofs and collapses loses its air pockets and absorbs oil. Roll the dough out to a thickness of 1 cm; when a thick piece is done on the outside, the inside may still be raw.
The frying setup also affects oil absorption. Use enough oil in the pot for the pieces to float, at least 3–4 cm deep; in too little oil, the dough sits on the bottom and absorbs oil on that side. Fry only a few pieces at a time, because overcrowding the pot lowers the oil temperature. Wait for the oil to heat back up after each batch. Flip each piece one time in the oil, and remove it when the 2 sides are golden; flipping it frequently interferes with the dough puffing up.
Do not pile the fried pieces on paper towels; arrange them in a single layer on a wire rack so excess oil can drip off. Pieces stacked on top of each other soften in their own steam. Making a small hole in the center of each piece with your finger lets heat reach the middle faster and reduces the chance that the inside will stay doughy. As the dough sits, it softens and becomes more prone to absorbing oil, so fry it soon after rolling it out. Add salt or powdered sugar when serving. When frying is finished, remove the pot from the heat and let the oil cool.