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)

I believe you might be looking for Cartellate, or Honey Pinwheels? Check this site out and see if they look familiar. http://www.mangiabenepasta.com/cartellate.html There are a lot of different recipes for them, but some of what I came across look like what you were describing.

It sounds like the cookie my family makes. we call it a dudela it is a dough that gets rolled on a grater then deep fried and soaks in honey with an orange peel.

I make a cookie like that. Our family calls it Conalicle. I it rolled and deep fried, then can be covered in Honey or heated caro. If your still looking for the recipe, I have it. I also have a picture, but it is too large to post here.

Maybe you are thinking about Krumiri? They are very popular in Italy.

my family calls them sculeete, but not sure that is the right spelling. Ours were braided and had whiskey, ginger, etc