In addition to @LatinSuD's suggestion of using grep's -m flag to stop reading after a match, you can adjust xrandr's output 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

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