First of all... This is not an easy question and IMO there are MANY possible scenarios... Depending on the code you developed, the packages you're using, the version you want to use, and so on...
Anyway This is what I would do in this situation:
Let's say for example I want to upgrade from version X to version Z where Z is two major / minor releases ahead of X
Step 1
Follow the next steps for one major / minor realease at time. Once I've tried to upgrade an application from Laravel 5.4 to 5.6 and it was completely broken. So I decided to upgrade to 5.5 and test the everything was working and, in case, block at that release. Luckily when I've upgraded from 5.5 to 5.6 (after code fix) I've managed to make everything work as it should.
Step 2
Upgrade the core framework and the plugins, check for errors during the upgrade and ofc, check the official documentation for any kind of compatibility problem
Step 3
Laravel has it's own upgrade guide that should be followed step by step. A good chunk of errors can be solved simply following that guide. There may be some plugins that doesn't provide it but usually the problems are releated to new features... It's hard that a method, class or trait has completely changed from one version to another.
Step 4
This step can be omitted, but from the example you've provided maybe it's better to add it. When there is a new feature that requires a specific class or trait or whatsoever, the simplest way to check if the error is thrown because of a file missing (and that is part of the "boilerplate") or has a different nature, is to create an empty project with that specific version and make a comparison with the "default" files.
For example, if you made no changes to the LoginController
, checking if the new version has any kind of updates, may be the solution.