I think what you are looking for is "fenekia". A farina based dough with little sugar, oil and often coated with or dipped in honey.
I think it's a Venetian specialty...or maybe I just think so because I had them in Venice.
I am sure there are many recipes on the web.
Linda C

Fenekia is Greek, not Venetian, from what I have found in my cookbooks.

Here is one that you may be able to alter by omitting the glaze and rolling in cinnamon and sugar, Westelle.

Tosca Cookies
Source:1001 Cookie Recipes

1 cup all-purpose flour
1/3 cup almonds, ground
1/3 cup farina cereal, such as Cream of Wheat
1/2 teaspoon baking powder
1 cup vegetable shortening
2/3 cup granulated sugar
1 large egg

Glaze
4 tablespoons butter, melted
6 tablespoons granulated sugar
1 teaspoon corn syrup
1/3 cup slivered almonds

1. Combine the flour almonds, farina and baking powder.
2. In a large bowl, cream the vegetable shortening and sugar. Beat in the egg. Gradually blend in the dry ingredients. Cover and chill for 2 hours.
3. Preheat the oven to 350 degrees. Lightly grease 2 baking sheets.
4. To make the glaze, combine the utter, sugar, and corn syrup in a small bowl and beat until smooth.
5. Drop the dough by spoonfuls 1 1/2 inches apart onto the prepared baking sheets.
6. Bake for 10 to 12 minutes, just until lightly colored. Brush the cookies with the glaze, sprinkle with the slivered almonds, and bake for 5 minutes longer. Transfer to wire racks to cool.

Here's an Italian cookie recipe I found. The word Farina is also often used to mean semolina in Italian cooking.
And perhaps the Italian neighbor was adopting a recipe given her by a Greek friend.
Linda C

Farina Cookies
This is a cookie recipe handed down from my great-grandmom Farina (no relation to the cereal people). Very quick and easy to make. Great for kids - not a lot of sugar!
by Rita OBrien

12 servings 24 cookies 20 min 5 min prep

3/4 cup butter
3/4 cup sugar
1 large egg
1 teaspoon vanilla
1 1/2 cups sifted flour
1 teaspoon baking powder
1/4 teaspoon salt
1/2 cup farina
1/2 cup raisins

Cream together butter and sugar; add egg.
Add remaining ingredients and stir.
Drop onto cookie sheet with spoon.
Bake at preheated 350° oven for 15 minutes.