You verbally accept a job offer but, shortly after, another comes in.
It's the one you want. How do you handle the situation to take the job you want but limit the fallout?
First, getting multiple job offers is a great problem to have. Ideally, you want your offers to materialize at roughly the same time so you can make your decision without having to back out later. But, it doesn't always work out the way we want.
Second, there is no reason to shackle yourself to an opportunity if you've just verbally accepted. Employers do the same thing quite frequently and will pull an offer if something changes on their end. You shouldn't lie awake at night with feelings of guilt for accepting a better offer. If you've signed an employment agreement, though, you will want to get some legal guidance on what the ramifications might be if you back out.
Most importantly, be sure to bow out gracefully. Communicate with the first employer as soon as possible to let them know. Yes, there will be some initial hard feelings. But, if you handle it professionally they will move on and think little of it.