I often make a second pot of tea from the leaves in the first pot - as you say, nice and thriftyBritesea said:You could try growing Camellia sinensis (tea plant), although if you live in a cold climate it will have to live indoors or greenhouse. The fermentation process to make black tea might be too much trouble, but green tea is simply a matter of drying the leaves. One old chinese fella I knew told me that he could reuse the same green leaves (he got them as whole leaf) for pots of tea all day long-- sounds nice and thrifty!
Might be a little harder to grow coffee- I suspect you would need more than one tree to make a decent amount of coffee.
