Exact same thing happened to me. Only a small part of the clutch lever broke, about 2 inches long. Seems to be made that way to break in case of fall, as there is a small groove. My clutch lever still functions fine. My dealer quoted me for about 50 bucks for the lever, not including labour cost. I'm looking at other options too.
At this point I doubt you'll find cheaper options than buying the OEM lever. If your dealer won't go down the price then just google "BMW 32728388835" and a choice of places to order it will pop out. $30-40 should do it.
If your dealer wants too much $ to your taste for a 5 minute job, then let's do it yourself:
1- Unscrew lock nut of tension adjuster. Screw-in the tension adjuster on lever to give you more free play and ease the job...
2- Unscrew the pivot bolt.
3- Remove the broken lever and free the tip of the cable.
4- Replace tip of cable inside new lever and put back new lever in place.
5- Redo step 2 and 1 in reverse order...
7- Keep old lever as spare - it's still working after all.
Here's a youtube video, not G310R specific, but any cable operated clutch lever is quite similar in design from bike to bike, so you can expect a very similar procedure.