Like this? This one is from Magma so is pricier but does just what your looking for. With this set up the probe isn't inside the pot, there is a nut welded center bottom on the outside of the pot, the sensor attaches to this nut with a bolt.
The up-down arrows set the desired temp (red numbers) and the actual pot temp is displayed with the green numbers. When the set temp is reached the heating element turns off, when the temp lowers back to the set temp it turns back on.
For comparison, all three of my mechanical thermometers normally stay within about 15 degrees of the digital temp.
Rick