Unfortunately, this is normal and expected for your big file use case. Your case of two hard disks, and a 50GB+ file eliminates a lot of misleading talk of "slow devices", "slow buses", and "slow filesystems", and you are left with the unexplained problem of a slow copy. You must have quite a bit of memory to get the performance you have for 30GB files. System buffers are used, filled up, and after your copy command finishes, eventually will get flushed to the target, making real timing/rates somewhat difficult (even the "time" command will finish long before the buffers finally get flushed.
The only "workaround" I have found is to use a "copy" command which allows you to set up explicit buffers yourself, like tar or cpio can do. Setting a 2MB buffer on tar allowed me to speed up a 10MB/sec copy of a 50G file to about 35MB/sec -- still much slower than the nominal 100MB/sec I get on smaller files (or in Windows).
Another workaround which may be a better solution is to install the nocache package and use nocache cp file target to limit filling the system buffers and dragging the system to a crawl. A 43G file copy to /dev/null ran at 53MB/sec, better than the large buffer for a tar copy.
Some disks, using Shingled Magnetic Recording (SMR) become really slow for large writes. If you copy speed is really low, but you still have lots of free memory buffers, this may be the cause.
Specific situations may be helped by settings for swappiness, vm_dirty bytes/ratio, renice, ionice, nocache, pre-allocating file space, scheduling,... but the basic problem remains that a system cannot work well without enough free memory.
It's probably crappy USB drive. Cheap USB drives have a write speed of <15MB/s, some as low as 1-2MB/s. Want faster? Buy an more expensive one.
10 minutes for 2GB works out to approx. 3.3MB/s, which is reasonable for a cheap drive.
The reason it show a quick progress is memory caching. The file is only written at the end of the copy process, which tricks the UI into believing that copying is further along than it actually is.
(As a sidenote: I've even seen drives advertised as USB 3.0... and 5MB/s write speed!)
First of all: Check your Files icon in the launcher (on your left for most systems). There will be a little progress bar over if it if it's still copying something.
In that case, if you're lucky, you can restore it in tree ways:
Look for a file copy icon in your system tray (upper right in most systems). If there's one, click it and the file transfer dialog will reopen
Right click on the Files icon in the launcher (yes, the one with progress bar on it) and choose "show copy window"
On your Files icon in your system tray (the one with a progress bar) are some small arrows in its left, one for each window. If you manage to click in the arrow, the corresponding window will open. Your copy window might be one of those
In the case none of this work for you, you might be seeing this bug