How do I get proportional 240V AC output from an Arduino-based PID controller to "dim" a rice cooker for a Sous-Vide project?
No need to use a PID. You can have a much simpler hysteresis control. 

Thermal capacity of water is around  $$4184 J/(kg·K)$$
In my case, the heater´s power was actually $$2kW = 2kJ/s$$
This means, it heats 1kg of water for about 0.5 K per second. In my case, 2kg water usually.

The bigger problem is precise measurement of the water temperature because of thermal convection. You want a circulator in there to keep thermal differences minimal. 

Once you have established good measurement, you can do a simple hysteresis control, in my case I switched the heater on with a mechanical relays for 1s to have a 0.25 K rise.

Temp reading error is going to be around 0.5 K anyways, so don't bother with too much of a regulation.

For a purely resistive load, you will be fine with a simple relays, which also does the electrical isolation for you. 

If you want to go for electronic switches, an optotriac will be just fine.