Verb. - To answer a question with "What?" not because you misheard, but because you need a moment to process the information or think of an answer while the person repeats themselves. May be done multiple times in succession. Often a knee-jerk reaction.
Noun. - The action of stall-whatting.
Jainy didn't know how to explain the broken vase; she had to stall-what Mom like three times in a row when she asked her.
When Lorraine asked me if we were going out, I was so shocked I did a reflex stall-what.