I've just been cutting more dies for my 4" Brent extruder barrel. I roll out a fairly thick slab of clay, about 1/2" thick, and then cut a circle which is slightly larger that the 2-handled die holder, made of aluminum in the first picture. After the clay circles have dried to leather-hard, and using brass hole cutters, I 'outline' the form which will be the hole through which the clay will pass, and then I 'connect the dots (holes)" to make the opening. In the second photo, you can also see the back side, --the side which the clay hits first--, which has been opened up more with a bevelling cut around the hole, allowing the clay to pass across a more refined line as it exits the die/extruder. I fire the dies to cone 2 (and am using Rovin's RO82m clay body). The strength of the clay allows me to use the die over and over, and the ease of making a new die is so accessible that I can do one in relatively short time. (the little 'D' shapped die in the first photo was made from some scrap clay I didn't want to throw away. With the large metal washers I can block off the open area so that only the small opening is used for the extrusion.)
