When boiling, you don't care about temperature. You need to control the duty cycle of the heating element, which is a fancy term indicating the % time it's on.
For example, if your element was turned on for 7 seconds, then off 3 seconds, that's a duty cycle of 70% (7/10). Another fancy term is Pulse Width Modulation (PWM), which is simply controlling the power to something by controlling the duty cycle.
You probably are wondering "why not just lower the power to the element"? Regulating that much power is not simple due to the huge heat dissipation that would result. Alternatively, turning it on and off (i.e., PWM) is really simple.
You need a PID with a manual mode (i.e., Auber SYL-2352) or a simple PWM ckt. These things allow you to set the duty cycle. Either way, this controller needs to be connected to a solid state relay (SSR), which is a big electronic switch that can be controlled with a small signal.
Now there's some take delight in the carriages a rolling
and others take delight in the hurling and the bowling
but I take delight in the juice of the barley
and courting pretty fair maids in the morning bright and early