You can download the BIOS update as an .exe file from Dell's support website. In my case, running it would just throw the computer into a black screen and not do anything.
First, to escape from the black screen error, hold down the power button to turn it off. Release, then hold it down again for 10 seconds to power it back on normally. The 10 second depress apparently resets something.
You can install the BIOS update through the pre-OS BIOS interface.
Prepare for it by copying the file to the partition first. How? Run CMD as administrator, enter "mountvol X: /s". This will mount the EFI partition on drive X. You can't access it via Explorer but you can still access it through CMD. Use the copy command to copy the bios update exe file to the EFI partition.
Restart and hit F12 during the Dell logo start screen. Select BIOS update, find the update file you copied to your EFI partition and voila!