I'm sorry you missed the point. Some letters are worthy of response. The one described here likely is not.
I think you're the one who missed the point. You suggested that the letter should have been trashed. That's a problem as it relates to insurance coverage. And, as I said, whether the letter warrants a response is for the OP's insurer to decide.
So basically what happened is that the damages are 2,500 above what my insurance covers. My question is now whether this will come out of my personal assets(Which I'm more than capable of paying), or if the money comes out of his underinsured driver coverage. And if I do have to pay, do I resolve this out of court(I really don't want this to go to court)?
Several things are important to understand.
If you get sued and lose, you're liable for 100% of the other driver's damages. Your insurance owes you a duty of indemnity and will pay any judgment up to the limit of your policy. If that's not enough to cover the entire judgment, then you'll have to pay it out of pocket.
If the other driver happens to have uninsured/underinsured motorist ("UM/UIM") coverage, then that coverage would pay the other driver for any portion of the damages not covered by your insurance. However, (1) that wouldn't get you off the hook because the other driver's insurer would
subrogate to its insured's rights against you, so you'd have to pay back the other driver's insurer; and (2) UM/UIM coverage is commonly available for personal injuries but is comparatively rare for property damage.
Your insurer owes you a duty to try and settle any claim within the limits of your policy.
Lastly, sounds like you should give serious consideration to increasing your liability coverage limits.
Shouldn't I start consulting with an attorney?
No. Turn this over to your insurance carrier. This is why you have auto insurance. If it is necessary to obtain an attorney, your insurer will hire one. That's a significant part of what you buy when you carry liability insurance.
And, I'll say it in no uncertain terms. Sitting by and ignoring this and waiting to be sued would be
phenomenally stupid.