In addition to @LatinSuD's suggestion of using grep's -m flag to stop reading after a match, you can adjust the size of xrandr's stdout buffer with a tool like stdbuf like so:
BRIGHTNESS=`stdbuf -o0 xrandr --verbose | grep -m 1 -i brightness | cut -f2 -d ' '`
This can give you a significant speed increase:
$ cat brightness
xrandr --verbose | grep -m 1 -i brightness | cut -f2 -d ' '
$ time sh brightness > /dev/null
sh brightness > /dev/null 0.00s user 0.00s system 1% cpu 0.485 total
$ cat brightness_nobuffer
stdbuf -o0 xrandr --verbose | grep -m 1 -i brightness | cut -f2 -d ' '
[ para ~ . ]$ time sh brightness_nobuffer > /dev/null
sh brightness_nobuffer > /dev/null 0.01s user 0.01s system 10% cpu 0.130 total