Restoring the EFI entries is as easy as running these from live boot:
mount /dev/<rootpart> /mnt
mount /dev/<efipart> /mnt/boot/efi
for i in /dev /sys /proc; do mount --bind $i /mnt$i; done
chroot /mnt
sudo grub-install
sudo update-grub
for anybody wanting to upgrade BIOS after installing any linux distro.