I would take a guess that the coil is doing something to a magnetostrictive ferrite, and this is transmitted to the milk and used to get a resonant pulse that is dependant in things like temperature ( likely read by a thermistor) and then the piezo discs on the ends read the oscillation to get the amplitude and such, which will be a function of the density of the surrounding fluid. Thus with the density and temperature you can calculate the amount of fat in the mix, thus giving butterfat and water content. Likely the piezo strips are used to do do a simple speed of flight to compensate the long rod, and the brass core is used to detect ionic concentration by the loss from eddy currents in the liquid.
But, without knowing the materials the ferrite is made from, you will not be able to copy the sensor, and will have to buy a new one. The materials are not likely to be off the shelf ones, and will probably be a proprietary blend especially made for the application.