The Form 1099-R that you receive for the distribution will exclude from the taxable amount in box 2a the NUA and the NUA will appear in box 6. The result is that, with regard to these shares, only the cost basis of these shares will be taxable.
It's your responsibility to track the cost basis of these shares because the brokerage will treat these distributed shares as noncovered shares. When you eventually sell these shares, you'll likely need to provide the cost basis of these shares yourself. The IRS does not track anything regarding cost basis of property.