Since writing this post, TypeScript has become officially supported in Laravel Mix (version
0.12 and up). There's still some informative stuff in here if you're new to TypeScript, but use the official method if you're on a newer version of Mix!
In a recent Spatie project we decided to give TypeScript a shot for the business critical part of a new application. TypeScript provides static analysis to reduce the chance of introducing bugs, to have self-documenting code, and to improve our tooling (autocompletion!)