In a wide frying pan, heat enough cooking oil to reach a depth of at least three inches.
Spoon the pâte à choux into a piping bag fitted with a large star tip. Press to remove air pockets. Don't panic if the pâte à choux doesn't fit into the piping bag. You will refill the piping bag later.
Pipe the dough directly into the hot oil. There are two ways to do this. With one hand holding the piping bag and another holding a pair of kitchen scissors, you pipe the dough with one hand and cut it with the other. Roll the strips around in the oil for even browning.
The second way is to pipe the dough in an unbroken spiral and do the cutting after the dough is cooked. Cook the dough in the hot oil until golden brown and crisp outside.
Flip the whole thing over halfway through the frying.
The churros are done when they are browned and crisp. Drain the fried churros on a rack.
Refill the piping bag and pipe into the oil once more. Repeat until all the pâte à choux has been cooked.
If you cooked your churros in a spiral, cut into three-to-four-inch sticks.
For the chocolate dipping sauce, measure equal amounts of milk and chopped dark chocolate. Heat the milk to barely simmering and pour over the chocolate. Stir until the chocolate melts.