“Parched” is among the Hundred Thousand, but our form “parchingly” is not (nor is “parch”, although “parching” is!).  “Parchingly” is a derivative form attested in the 1800s, and here’s our quotation:

1851   H. Melville Moby-Dick ci. 497   Most statistical tables are parchingly dry in the reading.

I believe that Mr. Melville and I have different tastes.  Not only do I love myself a good logarithm table or a nice analysis of variance to while away the long winter nights, I find Mr. Melville himself a bit sere.  I may have written a few rash things in a high school English essay on the subject.

• 08.046 that they were also parchingly thirsty,

Update 2016.06.28: I am adding the “food” tag, as the word is related to thirst and  nothing else.

“parching, adj.” OED Online. Oxford University Press, March 2015. Web. 1 June 2015.