Heat milk and cream. Heat the milk, cream, and ½ cup of sugar in a saucepan over medium heat until warm and steaming, or about 170 degrees.
Beat eggs and sugar. Meanwhile, beat the egg yolks and the remaining ¼ cup of sugar until light yellow in color and well combined. They will noticeably change color when mixed enough. (A hand mixer on low will work well.)
Temper eggs. Add half of the warm milk mixture, a half cup at a time, to the eggs and stir. Then add the egg mixture back into the saucepan with the rest of the milk and cream.
Heat custard. Heat the combined mixture over medium heat, stirring constantly, until it reaches 185℉. The custard is ready when it has thickened enough to coat the back of a spoon. Do not boil. Once off the heat, add a pinch of salt, and the vanilla extract, if using.
Strain and chill. Hold cheesecloth or a strainer over a bowl to strain the custard. Immediately place the custard into the refrigerator to chill. Chill for 4-24 hours, until very cold.
Churn and add chocolate chips. Put the cold custard in your ice cream maker and spin it according to the manufacturer's instructions until it becomes smooth and creamy. When it has reached the consistency of soft-serve ice cream, add chocolate chips and let the machine stir them in. Place the mixture into a loaf pan, cover with plastic wrap, and freeze until firm. It will keep well, covered in the freezer for a week.