Application notes and sources for supplying a Micrcontroller in a power supply
the NCP785A from On Semiconductor might be a solution for you. It is a Linear Regulator with an extremely wide input voltage rage of up to 450V. A simple diode and capacitor at the input is sufficient for rectification of AC. The drawback is: it delivers only 10mA. But if you calculate the amount of energy needed by the micro-controller for the start-up sequence, then you can calculate the necessary value of the output capacitor to hold the voltage during that time. Because the operating rage of the µC is quite large (1.71 to 3.6 V), this should be feasible.