The screenshots you linked to show quite a comprehensive web interface.
As a result I think you should do the browser based human interface on a PC.
The Arduino could be used to autonomously run a control sequence for the brewery i.e. when the PC is off the Arduino continues to run the control sequence last downloaded to it from the PC.
One thing you have not mentioned is whether or not you wish to record what happens during the brewing sequence. If you do then you need to consider where the data will be stored e.g. if the PC is not 'on' all the time then you would need to store data on the Arduino and upload it to the PC when a connection is established.
So it is all possible but a good deal of thought needs to go into what information is communicated between the PC and the Arduino and when.
You mentioned that the existing system is "not quite suitable" for you. It would probably be a good idea to say why, to see if the Arduino eliminates those issues.