UART Modulation Using STM32
You could use an Exclusive OR like the 74AHC86 - it's a Schmitt trigger type and if you feed the uart input to both inputs but have an RC delay on one of the inputs (say 10us), you'll get a 10us pulse each time the uart output changes state. 

I think 100us (as per your question is too long for most common bitrates - 9600bps has a bit period of 104us so any faster will be a problem - that's why I suggested 10us (R is 10k ohm and C is about 1nF).

This is a fairly standard method of clock recovery on synchronous systems by the way.