Microprocessor modules in series
No it is not possible. As already said, it is a variable voltage and more than that if the two microcontrollers have to communicate or even communicate with the same other device, ground would not be the same it would be a complete mess. I don't really kjnow what would happen.

What you can do is : instead of using a linear regulator to drop from 12V to 3.3V, use a DC/DC switching regulator . The difference is that the DC/DC works in power mode and not in current mode like the linear regulator.

For the linear regulator if you have 500mA on the 12V you have 500mA on the 3.3V.

For the DC/DC if you have 12*500mA = 6W at the output of the solar panel you will have the same power on the 3.3V which give you a current of 6/3.3 = 1.8A. And you will be able to power both your microcontroller.

This type of DC/DC should do the job, it is just an example there is probably other DC/DC module matching your need http://www.ti.com/lit/ds/symlink/tps63061.pdf