How do lasers measure short distances (<1cm) when electronics are too slow for time-of-flight to work?
At 2mm, time-of-flight is not used. Interferometry is. Unlike time-of-flight which can only really determine distance (and velocity indirectly), interferometry can be used for measuring many other properties and has a much higher sampling rate. Some amazing things have been done using this principle including LIGO or verify the influence of Earth's gravity on the speed of photons travelling towards and away from the Earth's surface. Or eavesdropping on someone from outside the house by measuring the vibrations of something in the room.

Interferometry most directly measures velocity. It's a bit less straightforward to measure distance.

You can play with this yourself fairly simply (as long as you have an oscilloscope) using the self-mixing technique which requires a laser diode with an integrated monitor diode, otherwise you need a lot of expensive optics which then puts it beyond reach of your typical hobbiest.

It's super cool. You should try it. The required laser diodes with integrated photodiode can be bought for a few dollars (1/10th the regular price) if you look at surplus electronic shops like Jameco, rather than places like Mouser or Digikey. Just make sure to check the datasheet to ensure that there is a photodiode inside. You also don't want a laser module that might already be wired to monitor the photodiode to maintain constant optical power since you need access to the laser diode.

Layman video demonstration:
https://www.youtube.com/watch?v=MUdro-6u2Zg

A paper which makes a lot more sense after watching the video if you're not already in the know:
http://sci-hub.tw/http://iopscience.iop.org/article/10.1088/1464-4258/4/6/371/pdf which can also be read in semanticscholar.org and is paywalled here. Giuliani et al. J. Opt. A: Pure Appl. Opt. 4 (2002) S283–S294