Fine, coarse adjustment digitally
It's not clear why you want to do this. The Arduino, which you mentioned in other posts, has a 16-bit PWM timer and you can learn how to use that in the answer to increase-pwm-bit-resolution.

Your cascaded potentiometer arrangement is poor. Imagine what happens when the first pot is close to maximum. The second one then spans the whole range so you have lost any advantage of having two pots.







simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. A coarse (R2) and fine (R1) potentiometer arrangement can use standard single-turn pots. With the 1:10 arrangement shown the fine adjustment would be about 1/10 of the coarse adjustment.