What is this Italian Cookie called?
Gnocchi shaped?  I am pretty sure they are  Turdilli! .  

It's a traditional Calabrian recipe:  



They are deep-fried: 





And hot-soaked in honey too:

  

Same biscotti, slightly different shapes: 





Bear in mind that fried cookies soaked in honey are a traditional treat for carnival and Christmas seasons all over Italy, so you may find many, many similar recipes. From  http://www.marinacepedafuentes.com/2010_02_01_archive.html :  


Evviva i Dolci di Carnevale rigorosamente fritti, che ricevono nomi diversi secondo i luoghi.
In Toscana chiacchiere o trecce, e poi frappe laziali, castagnole romane, frittelle di riso molisane, fritole triestine, nigelan altoatesini, sfincitelle siciliane, tortelli romagnoli, bomboloni fiorentini, cicerchiata umbra e chi più ne ha più ne metta!
  

At left with figs syrup, at right with honey:  



A full blown italian fritti feast:   



Turdilli recipes in Italian

Turdilli recipes in English

Video: Making Turdilli

A shop near my house sells turdilli (hold your envy)