People often forget that work is work. A career where everything is engaging/fresh/challenging at all times does not exist. The challenge is to find a way to nurture those aspects in the job we have, or find a job that, with realistic expectations, satisfies us. For example, most despise anything tax related, but there are those who have a passion about taxes that I wish I had about anything. But I'm sure even a passionate taxman has something about that job that bores him. Conversely, a Bricklayer who discovers that he hates laying brick, should probably move on. Otherwise, it really comes down to attitude.
There is a chance those 'existing' tasks are exciting because you aren't working on them.
It sounds like OP has passed the 'in-love' stage of this position. When we start new jobs, usually things are fresh and exciting. You cannot expect that those feelings will last the entire duration of your career. Even in the most varied project-based positions, exciting projects will come and go. Even the ever changing jobs may appear repetitive or mundane to a senior employee. People who try and chase the rush are the ones who are constantly changing from one position to another. We see the passion in them at first, but as their exciting tasks become routine they quickly tire of it. Ironic because you are only providing your full value to your employer after being trained in the defined role. I say again, Work is Work. Do your job, and be patient. Eventually something will keep the fire lit.
All that being said;
1) Ask your boss for something more challenging/engaging/outside your comfort zone. Most managers will appreciate this initiative and honesty. Worst response will be "get back to work", best case you get something that satisfies your needs. Note: be careful what you wish for, new challenges have the same risks mentioned above.
2) Try and find excitement in the mundane. I like tracking my time completing repetitive tasks and doing everything in my power to best it. Try to eliminate all inefficiencies associated with said task, you're wanted to get it off your plate asap anyway. Or try finding process improvements that will circumvent the task altogether.
3) Ask if there are any employee developments that the company would be willing to enroll you in or resources that may help further develop. Most of my excitement comes from extracurriculars provided by the company, or externally.
4) Be the best at what you do. There is an power that comes from being the best [position name] the company ever had. To be the one that everyone talks about years after you've moved on. To be painfully missed when you take vacation. Striving for this will motivate you to process the mundane, unexciting stuff better than anyone before, or afterward. Added benefit: there is job security in taking the tasks that have to be done, but most don't want (and being the best to do it).
5) Buck up & Knuckle down. Wait for the golden nuggets to trinkle your way, if they don't, see #1.