How can I reinstall GRUB to the EFI partition?

Reinstall the GRUB boot loader to your Ubuntu installation in EFI mode this way ...

Boot from the Ubuntu installation medium and select 'Try Ubuntu without installing'.
(Boot your install medium in EFI mode, select the Ubuntu entry with UEFI in front.)

Once you are on the Live desktop, open a terminal and execute these commands :

sudo mount /dev/sdXY /mnt
sudo mount /dev/sdXX /mnt/boot/efi
for i in /dev /dev/pts /proc /sys /run; do sudo mount -B $i /mnt$i; done
sudo chroot /mnt
grub-install /dev/sdX
update-grub  

Note : sdX = disk | sdXX = efi partition | sdXY = system partition

To identify the partitions use GParted, the tool is included in the installation medium.
After having run the commands GRUB will be installed in the separate EFI partition.

this is the only way that worked for me: (System: sdb8, boot: sdb6, efi: sdb2)

sudo mount /dev/sdb8 /mnt 
sudo mount /dev/sdb6 /mnt/boot 
sudo mount /dev/sdb2 /mnt/boot/efi

sudo mount --bind /dev /mnt/dev &&
sudo mount --bind /dev/pts /mnt/dev/pts &&
sudo mount --bind /proc /mnt/proc &&
sudo mount --bind /sys /mnt/sys

sudo chroot /mnt

grub-install --target=x86_64-efi /dev/sdb

grub-install --recheck /dev/sdb

exit &&
sudo umount /mnt/sys &&
sudo umount /mnt/proc &&
sudo umount /mnt/dev/pts &&
sudo umount /mnt/dev &&
sudo umount /mnt

Thanks to @cl-netbox for the instructions!

After I upgraded (Linux Mint 18.2 Sonya to 18.3 Sylvia) my system wouldn't boot so I followed the instructions above but still no success. I noticed however that my machine has /boot in a separate partition (possibly because I am using LVM) so my slightly modified process was:

sudo mount /dev/sdXXX /mnt
sudo mount /dev/sdXY /mnt/boot
sudo mount /dev/sdXX /mnt/boot/efi
for i in /dev /dev/pts /proc /sys /run; do sudo mount -B $i /mnt$i; done
sudo chroot /mnt
grub-install /dev/sdX
update-grub 

Note : sdX = disk | sdXX = efi partition | sdXY = boot partition | sdXXX = system partition