Updating kernel versions when booting from rEFInd

I'm booting from EFI using the awesome rEFInd bootloader. I've so far had to configure boot myself by manually copying over my EFI-compatible linux boot image to my EFI partition and writing a configuration file to define a rEFInd menu entry and link to the specific kernel image on the EFI volume. GRUB, on the other hand, adds new kernel versions as they're installed and I always boot into the new kernel on next boot. It accomplishes this via the update-grub script, I believe. Is there another script I can call into to automatically deploy new kernel images to my EFI partition and ensure they're available on next boot? I'd like to automate this process as much as possible so I'm always getting the latest kernel security updates.