I would like to use it as kind of a trigger / controller for example...
With slow turning the handle of the grinder I would like to play my sound composition and control the speed. So when I turn the handle slower or faster, it affects the speed. So it would be nice to have sensitive readings.
I'm just thinking now, what sensor / technique I should use...
There's two problems to be solved here: Mechanical and Electrical.
Electrical. How many pulses per revolution do you require for "smooth"? You're playing a tune and you probably want only 5 or 6 notes per revolution of the handle. Maybe double that for semi-quavers. So 12 pulses per revolution would be just fine for your purpose.
Do you want it to play the tune backwards when you wind the handle backwards? Or just any movement of the handle will advance the tune?
Mechanical. How to hide an encoder inside an object that's already built. First, does it have coffee in it? Is it still supposed to function for its original purpose? That makes it more difficult.
I would consider a belt-drive from the main shaft to a small shaft encoder. The belt can be a rubber band.
Alternatively, you could probably put an encoder disk in there and use an optical encoder looking at the disc. Print a pattern of black and white radial bars on your home printer and cut that paper out in a circle. Use a QRE1113 reflective sensor. Sparkfun has two breakouts for these, which will probably fit inside the pictured grinder. Choose the "analog" version. It is much easier to work with.
If you need direction, to play backwards, look up "quadrature encoder" and build your own with two QRE1113 sensors looking at the one disk.
It sounds as a good plan. Will try your suggestion. I don't need to go backwards with the grinder. And there is no coffee and it does not need to be functional anymore. It is actually broken anyway:)