I think I may have been conceptualising this incorrectly.
Regardless what I actually wanted to do was pass a variable from a Blade template to a Vue Component, for anyone else who may have followed the same weird train of thought as I did this is how you do that.
First send your data from your controller to your view as you would normally. Check you can view the data in your Blade template.
Then, on the element that you wish to pass the data include your passed data like this:
<my-component :project = "{{ $project->toJson() }}"></my-component>
Then in your Vue component (called 'my-component')
props: ['project'],
data() {
return {
title: this.project.title,
};
},
Which you can then use however you want!
Phew, for some reason this tool me far too long to figure out, but I am very happy to say this is now working perfectly and just in the places I want it.