I just remembered that Charlie Poole recorded this even earlier - 1926. It has the exact line you mentioned.

HUNGRY HASH HOUSE

I'm a boarder and I dwell
In that second-class hotel
If I stay here long I think I'll go insane
For I lay here on my bunk
And I cannot get my trunk
For the board I owe would break a millionaire

Oh they feed on chicken pie
If you eat it you will die
Beef you cannot cut it with a sword
Oh the undertakers hang around
For there's work to be found
In that awful hungry hash house where I board

Oh they carried me upstairs one night
I had neither gun nor knife
Something they had never done before
Oh the fleas held me down
While the chinches crept around
In that awful hungry hash house where I board

Oh the beefsteak it was rare
And the butter had red hair
Baby had its feet both in the soup
Oh the eggs they would not match
If you touched one it would hatch
In that awful hungry hash house where I stay

Repeat last stanza twice.

Author is unknown, but its style suggests in may be of vaudeville origin.
Source: Charlie Poole and North Carolina Ramblers Co 15160-D. Recorded 20 September 1926. It has been reissued on 'The Legend of Charlie Poole Vol 3' County CD-3516

Other recordings were made in the 1920s by Ernest Stoneman, Uncle Dave Macon and Byrd Moore.
PS.

Cheers, Stewie.