Designing a power supply that drives an LED array supply
Wikipedia has some good examples about dimming.  For as simple solution as possible (by electrical terms) I would use a transformer, full wave DC bridge and a thyristor. Again, wikipedia has a great picture of that



Note that thyristor dimmers usually make some radio frequency noise but as I see it, this is one of the simplest AC dimmers. 

You will find more info about different dimmers on http://en.m.wikipedia.org/wiki/Light_dimmer

And although you would like to keep out from MCUs, at least think about them. If the thyristor-stuff goes over your head, try to use MCUs. You will find them to be very useful for your future projects.