LED matrix dimming: How to control the current in a 12V LED lamp for video lighting?
What about this: -



Here's the data sheet. Here's other devices that should do the same job.

Alternatively, if you are stuck with the LEDs being soldered as they are, a regular buck regulator would be OK but I'd recommend a power supply of nominally 15V: -



You can adjust the device to produce a lower-than-12V output by using a pot in the feedback to FB - note that there are two resistors feeding FB at the moment to produce an output of 12V - if you scaled there ratios down to more-or-less suit the value of your pot in place of the 619k resistor it would work but always have a little bit of resistance in series i.e. if you had a 50k pot then leave 2k2 in series so that the output never gets directly connected to the FB pin. Note FB means feedback.

Here's the LT search page I used for this.