If I have 27V at the top of the string of 9 LED with Vf of 2.7V (Vf total is 24.3) and a 41 ohm resistor:

27V-24.3V = 2.7V across the resistor

2.7V across a 41 ohm resistor is ~0.06585A

0.06585 * 0.06585 * 41 = 0.1778 W dissipated power

If I want half the brightness, I can double the resistor to 82 ohm

2.7V across a 82 ohm resistor is ~0.03292A

0.03292 * 0.03292 * 82 = 0.0888W dissipated power

0.0888W/0.1778W = 50% so at half brightness, there is half the dissipated power.

If I were to pwm this instead of using a variable resistor, how would it be more efficient?