Hello EProuty, and thanks for the great question.
Yes you can install the Laravel PHP framework on our shared hosting plans. It's pretty simple, just fire up the Softaculous installer after logging into cPanel.
In the search box towards the top-right, just search for Laravel and then click on the icon once it pops up. Then just click on the Install button and select where you would like to install it to.
Please let us know if you had any other questions at all!
- Jacob