What have you used for asset management before?
The fact that Phoenix by default installs with Brunch doesn’t mean it’s joined at the hip with it. For example the Static Assets Guide has a “Using Another Asset Management System in Phoenix” section that shows an example with Webpack 1. (See also How to plug in webpack 2.0 into phoenix 1.3.0-rc and https://github.com/gbih/phoenix-vue-bootstrap-postcss).
So rather than getting up to speed with Brunch, it may make more sense to integrate the asset management system you are already using (my personal impression is that Vue.js is rather webpack-philic and that Brunch may not keep up with the developments that Vue.js needs (e.g. vue-brunch is no longer being actively maintained) - Brunch works well enough for an EEx centric web application that uses modular JavaScript (e.g. for progressive enhancement) using npm as a package manager).
