Usually at larger companies, Branding and UX will be handled by different teams or designers who collaborate with one another to ensure their work is in alignment. However, for smaller companies or startups, it's common for one designer or team to handle both Branding and UX needs. If that's the situation you're in, it's important to first consider that these two types of design often have very different goals.
At a high level, the goal of Branding is communicate the ethos of a company, as well as remain recognizable and distinctive in a variety of scenarios. UX's goal is to ensure everything they create is intuitive and consistent. The overlap between the two in context of a website often times comes down to language/copy, UI, and illustration. That said, one doesn't necessarily need to come before the other.
For your situation, I'd suggest you begin to think about what is needed more immediately. For example, if your company is brand new, in a very competitive industry and hasn't yet determined what their mission and values are, then I'd suggest you start branding first as it will help inform the way you design your site. Conversely, if the company has been around for awhile, and kind of "figured itself out", has a clear product strategy, and is really only needing the visual aspects of branding (logo, colors, font, etc), then you can totally start the UX first.
Like most things in design, there's no "right way" to do this stuff – it almost always comes down to the context of the situation, the company, and your role.
Hope that helps a bit!