Behaviour of microphone with high volume input
An overview of the analog signal path in a system such as yours:



Clipping can take place:


In the microphone as mechanical soft clipping, distorting the waveform rather than clipping exactly at some value.
In the built-in impedance converter field effect transistor (FET) of the electret microphone capsule. (I think this is very much like hard clipping)
In a separate preamplifier as analog hard clipping.
At the analog-to-digital converter of the audio interface, as hard digital clipping.
On the digital signal if any digital processing is done on integer data, as hard digital clipping.


Because the clipping is hard at numerical values -1 and +1, digital clipping must be taking place. Because it looks like there is hard clipping also at other numerical values than -1 and +1, there is probably hard clipping taking place at more than one stages separated by an alternating current (AC) coupling. Blowing directly into the microphone is quite an extreme disturbance, so there is probably also the 1st and the 2nd kind of clipping going on.

There are a few places in your system where there can be an AC coupling or equivalent: 


In the microphone, as the pressure in the back of the omnidirectional closed-back capsule slowly equalizes with that of the outside world due to a (by design) leaky seal.
On the analog signal. AC coupling may be built in into the plug-in power supply to the microphone, into the preamp and into the audio interface.
Digitally in the audio interface or in the digital audio workstation (DAW). Check the settings!


If you blow into the microphone long enough then the AC coupling begins to see the average pressure level of that as direct current (DC), centering the signal to zero during the disturbance. When you stop blowing it takes some time for the coupling to adapt to the normal atmospheric pressure.

If you want the electronics to recover faster after a disturbance, try adding a capacitor in series with the signal output of the plug-in power supply as yet another stage of AC coupling. The capacitor should be small enough to make the time constant of the resulting resistor–capacitor (RC) filter short enough.