possible? Yes.
practical? No
consider how often you would be brewing, say once a week max. You would then need to either size you solar array to run the kettle in real time. Ie 2 - 3 kws in panels (basically a standard sized house installation). Or store enough energy in batteries and run off the batteries. Considering all the boiling I would guess 5kwh MINIMUM. That is quite a lot of battery.
The basic problem is that heating water is one of the most energy intensive things you can do, especially in the house. You are wanting to heat it up to a very high temperature in a short amount of time, so you cant even use the water itself as a store.
If you are interested in solar I would look into residential solar and net metering.
if you want to go off grid, go wood fired.
sorry for the downer, I'm sympathetic but cant think of a worse suited domestic activity to go solar with. Perhaps your fridge, or laptop /mobile phone? They're much more suitable if you want a project.