Take notice of a few things first:
1- Who creates the good opportunities?
If the star employee is doing all the cool stuff that was listed long ago or if management/clients do so independently from him, then we may proceed with the answers you might be expecting. Nonetheless, if your colleague is the one who comes up with the ideas for doing exciting things he can easily deliver, or maybe already started working on already, then he has a good claim on this kind of stuff. Up to you to make your entrepreneurial side shine in the company. Don't expect cool stuff to appear out of thin air and luckily fall on your lap.
2- Check qualifications and handicaps
Maybe said employee is someone who is crucial for the company on several accounts. Perhaps he is a partner or has lots of expertise in company-specific frameworks/code bases. If that is the case, then management has extra reasons to hand him motivating tasks. Otherwise, he might have some form of attention deficit that makes it very difficult to perform well in "manual labor". Maybe he's someone with a history of depression, so he could suffer a lot if given difficult/complex tasks or lose interest right away in the job if given menial tasks. People with depression should be managed in a very different way than most employees.
Then again, what about you? Are you up to the tasks that are being assigned to your colleague? Or would you have a hard time completing them timely, while your colleague has no problem with it? If you still lack experience and knowledge in the field, maybe do some more boring stuff while honing your skills. Cool and complex stuff will come up eventually your way. You don't earn the trust of management overnight unless they have no option but to rely on you, but time inevitably gives you opportunities to build your reputation.
3- All that being said...
Supposing that your star colleague is neither any better nor any worse than the rest of the team. Assuming that you at least have skills on par with him. Then you can talk to management, but be brief and show no resentment nor social conflict, something on the lines of:
Hey [manager name], I think [colleague name] does a good job on [project name], but I'd like to point all that this project has a mix of both fun and menial tasks, which is normal for any project. [Colleague name] has a lot of initiative on assuming fun tasks, but I think this may start degrading morale for the team over time. If you could mind this aspect of our tasks to promote a more balanced workload for everyone, I think this would be great.
A good manager that minds the happiness of his employees should understand the message that he's just not given a deserved attention to this aspect of the workplace and curb your colleague's monopoly on the fun stuff. If management is bad and ignores you, then go back to item 1. Else...
4- Speak up for yourself
Try claiming some of the good stuff by simply being the person with the most initiative. But if you want people to approach you directly with fun stuff, remember to accept and deliver when people approach you with boring stuff as well. This builds good relationships and reputation. When you want your problem solved, you go to the person you think will solve it and who you think will have the goodwill to do so, the same goes for management and colleagues at work.