Pressure cook the urad dal till it is soft. Run it through a food processor to make a coarse paste.
Mix with rice flour, cumin seeds, butter, salt and hing to form a pliable dough. Work the butter into the dough until it is fully incorporated while making the dough.
Gather 6-7 small steel plates or fold pieces of aluminum foil to make 5" squares and lay them out on a cutting board.
Heat the oil in a kadai until a small bit of dough dropped in the oil begins to bubble and rises to the top smoothly. Turn the heat down just a tiny bit at this point. Thengolu needs to be fried on a lower fire to keep its light brown color but cook through and crisp up.
Grease the chakli press and load a ball of dough into it. Working quickly press out the dough on to each of the steel plates or foil squares carefully using a circular motion and slice off the dough with your finger. Make sure to gently press any loose ends onto another piece of dough to keep them from unraveling in the oil.
Flip the thengolu dough gently from the plate one at a time onto a slotted spoon and then into the fire. Fry until the number of bubbles from the dough slows down and the thengolu turns a golden brown. Do not fry until it gets too deep in color. Do not overcrowd the oil.
I usually fry 2-3 test pieces, wait for them to cool for 5 minutes and check the texture. If it is too soft inside, turn down the fire even more and fry for a little longer. If it is too hard and brittle, mix 2-3 tbsp of the oil into the dough. Make sure to let the oil cool for 5 minutes before mixing into the dough.
Transfer the thengolu to a tray lined with paper towels. Once cool, they can be stored in an airtight container for several weeks.