Basil is an experimental theme for Magento 2 that uses the new GraphQL API to display the catalog. It is written with React, Next.js and Apollo. Currently, Basil only displays the catalog since the full checkout and customer management functionality has not been included in Magento's GraphQL API yet. The theme is just a prototype so it is not responsive and needs some code cleanup and unit tests, but I wanted to share what I have been able to build so far.
To see a preview of the theme, you can view https://basil.andrewdavis.me.
Basil has been licensed under AGPL so if you would like to use it for any of your own projects, your project must be open source under the same license as well.