Basically, they use the reactor to produce high-temperature water. Well above the boiling point, but kept in a state of supersaturated steam due to the immense pressures.
When the grounds are ready and the steam is up to temperature, the crew fires an explosive charge which propels a massive driver into the steam chamber. The already-high pressure in the chamber skyrockets, which causes a precision-machined "burst disk" to rupture.
The sudden loss in pressure causes the superheated water to flash almost entirely to steam, which raises the chamber pressure even more. This column of superhot, superdense steam is directed through what's essentially a "gun barrel" into the chamber containing the grounds, at transsonic speeds- upwards of 10K-12K km/h.
The grounds are soaked, stripped, cooked, crushed and pulverized by the incoming steam ram, stripping every last molecule of caffeine out of the beans.
After the impact, some of the pressure is bled off, the water collected and filtered, run through several heat exchangers to reduce the temperature to something slightly less than scalding (the waste heat is used to heat the swimming pools) and then pumped into a holding tank, where it's then distributed to the various break rooms and water fountains throughout the shop.
Serves about 20,000, or one particularly thirty polar bear.