Wow, that's definitely one that you should be thankful that the engineers at BMW got the design right on. I handled claims on damaged vehicles in my former career with Geico. If you have any questions about settlement, or insurance in general, hit me up. I'd be happy to help.
Edit: FWIW, I presume that you carry UM/UIM coverage on your policy. This coverage is optional! Check your policy in the declarations page, and it will tell you the limits of your coverage. If you see figures like 100,000-300,000, that's the policy limits on Bodily Injury. This pertains specifically to the policy limits for medical coverage. Uninsured Motorist/Under Insured Motorist deals with property damage, i.e. compensation for your vehicle loss. All insurance companies use comparative pricing when it comes to determining the FMV(Fair Market Value) for your car.
If it's paid for, make sure that you ask the adjuster how many "comps" they used. I know when I would adjust a claim, I'd aim to have no less than 4, depending on the vehicle. Honda Accords/Civics are a dime a dozen, so the comps are easy to use. Land Rover, Audi, etc. ehh, not so easy in my area. We don't use Kelly Blue Book pricing; that's for retail and private sale. Ask to see the CCC report; it takes into consideration the condition of the car, pre-existing damage, paint, glass condition, tires, interior, options, etc. There's about 45-60 different portions that go into calculation of the settlement offer. Keep in mind, you don't have to take the first offer, even though the adjuster will pressure you to try to do a quick settlement. It's understandable because part of our job is to handle the claim in an expedient fashion. Mainly because we have a metric fuck-ton of claims to handle, and we're understaffed in our area. But that's another story.
If you have a note on the car, your lender 99.9% of the time mandates that you carry Collision Coverage on your policy. If so, your policy will pay the lender the amount determined by the CCC report/adjuster's offer. If there is positive equity, you're in good shape. Your note is paid off, and you will get paid the balance. Use that money to make a down payment on another vehicle.
You said that the other driver is uninsured; that's a sad fact today. Lots of people take a risk when they drive uninsured. Hell, I'm guilty of having done it when I was younger. Either way, your policy will pay for the value of your car, and then the claim will go into "subrogation". They'll go after the other driver for compensation. Depending on state laws, they can get judgement to garnish wages, work out repayment plans, have the DMV suspend licenses, etc. If none of this happens, they'll write if off as a loss. But the policyholders who pay their premiums help absorb this cost. That's why premiums have increased over the past 2 decades.
If you have negative equity ("upside down"), you better pray that you purchased a separate Gap policy. Otherwise, you will be on the hook for the difference between the loan balance, and the offer from the Ins.Co.
I can elaborate if needed.