Some people sing this to the tune of Twinkle, Twinkle, Little Star (though another tune is sometimes used for this song)…

Bolli bolli pentolino - Italian Children's Songs - Italy - Mama Lisa's World: Children's Songs and Rhymes from Around the World  - Intro Image


Here's another version of this rhyme from Emanuela. She wrote, "This nursery rhyme is liked so much, and we always sing it before going to lunch with the three year old children. It goes like this:"

(Emanuela's note in Italian, "La filastrocca piace tanto, e noi la cantiamo sempre prima di andare a pranzo con i bambini di tre anni, continua così:")

Bolli bolli pentolino,
fa la pappa al mio bambino;
la rimescola la mamma
mentre il bimbo fa la nanna;
fa la nanna gioia mia
o la pappa scappa via.
Guarda, guarda
Il can(e) che scappa,
si é portato via la pappa,
l'ha portata via al bambino
per portarla al cagnolino!
Cagnolino, tutto contento,
se la magia in un momento,
se la mangia e fa bu, bu!
E la pappa non c'é più!
Più, più, più!

English Translation:

Boil, boil, little pot,
Cook the food for my baby.
Mommy mixes it
While the child goes to sleep.
Go to sleep, my joy,
Or your food will run away.
Look, look
At the dog that runs away,
It has taken away the baby food,
It has taken it away from the child
To bring it to the puppy!
The puppy, very happy
Eats it in a moment,
He eats it and goes boo boo!
And of the baby food there is no more,
More, more, more!

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Here's the 2nd part of the 2nd version recited...
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Thanks and Acknowledgements

Many thanks to Sarina Longin for the drawing! Thanks to Emanuela Marsura for sharing the rhyme! Translated by Emanuela and Lisa.