This is one of the problems that TDD tries to solve.
To make changes to a small piece of code, you don't want to have to go through a huge iteration of running up your server, going to your browser, moving around the app to get into the required state and then trying out the bit of functionality. No, you just write a test for that bit of code and run it. No browser needed.
The cycle he describes is what you do at the very end. Once.