Regulating the heating element for the boil kettle

On the boil kettle, I have a 4500w heating element. I don't have a temperature controller on it, its just a on off setting. For 10 gallons, it works fantastic. For 5 gallons, it's too powerful. I don't want to put a temperature controller on it, because I don't want it cutting on and off.

I'd rather be able to dial down the power. I know other people have this issue, but I don't know what to search for. A friend of mine recommended using a solid state relay, combined with arduino to accomplish everything. I'm curious what would be the simplest, and most cost effective method. Or just suggestions what to search for. Thanks!

Well with a SSR and arduino or a PID cycling the power on/off is exactly what you'd be doing. Is there a reason you don't want to do that? The elements can handle it no problem...

But what it sounds like you want is a PWM. Without further adieu: https://www.homebrewtalk.com/f170/pwm-show-us-how-221301/

Also search for voltage resistance ssr on eBay or amazon for a phase angle control.