I absolutely love cooking and absolutely love 3D printing and this project has been in my to-do list for way too long. I used the motor from my MK8 extruder and exchange it whenever I need it (it only takes a few minutes but I'm planning a quickswap hack to make it even easier).
The motor drives a small gear that moves a bigger gear (1:5 ratio) that is then attached to a threaded rod, giving a total torque gain of around 1:20, necessary to extrude pretty thick and viscous things.
The nut attaches to the plunger top via a 3D printed part, and the threaded rod goes between the "X" of the plunger body in order to save space. I made this for these 60ml syringes which were the largest I could find, and the only adaptation you need to make it to cut a little notch in the plunger top in order for the nut to fit. Because of this design, you can insert and remove the syringe easily by just popping it out.
And yes, you could probably use it with clay, but cmon, food!