My circuit was
12v Battery----1Kohm Linear Pot-----LED---500Ohm resistor---Ground
Let's assume that we are talking about the Blue channel, because that probably gives the largest Vf of around 3.2v
So with the pot dialled all the way back, you have 500R dropping 8.8v, 17.6mA, that seems a little low for "full bright".
With the pot dialled all the way in, you have 1500R dropping that 8.8v, 5.8mA, that seems a little high for "full dark".
So you might want to play with the values, reduce your fixed resistor, increase your potentiometer.
But dimming an LED just by limiting the current may not be the best way to do it, modern leds are fairly bright even at small currents so you'll likely find that there is a perception that the dimming isn't very fine, but rather granular (bright, not-quite-so-bright, pretty-much-off). PWM dimming will probably produce a better result. Grab a 555 timer, your 1k pot, and a couple of passives and make up a text book 555 pwm circuit. See how it compares.