Incandescent Light Bulb Soft Start
You can run LEBs (light emitting bulbs) with PWM.  In fact, soft start actually increases their lifetime.

It is possible to chop AC, but generally easier to rectify the AC then chop the resulting DC.  Four diodes and a capacitor are good enough to make DC to run the bulb from.  You also need to make a small low voltage supply to run the processor from.

The switch itself is probably most easily realized by a NPN transistor rated for the voltage.  It can be controlled directly from the low voltage output of the microcontroller PWM.

Note that the rectified DC will have a higher RMS voltage than the AC.  You compensate for that by not going to 100% duty cycle for full on.  You could even measure the DC and adjust the duty cycle on the fly to make the light intensity relatively insensitive to voltage fluctuations of the AC.  You could even make a "universal" powered light.  That's one that can run from 90 to 250 V, 50 to 60 Hz.