Barb, The cookie you are seeking I believe is Taralli.
Hope this helps you.

Taralli al Finocchio (Neapolitan Bread Rings)
Source: Celebrating Italy

2 1/2 tsp. active dry yeast (1 pkg.)
1 1/3 cups warm water
3 3/4 cups unbleached all-purpose flour
1/3 cup fennel seeds
1 tsp. sea salt
1 or 2 egg whites

Stir the yeast into the water in a large mixing bowl; let stand until creamy, about 10 minutes. Stir in the flour, fennel seeds, and salt until well blended. Knead on a floured surface until firm, solid and elastic, 8 to 10 minutes. Place the dough in an oiled bowl and let rise until doubled, about 1 1/2 hours.

On a lightly floured board, flatten the dough to a 12 by 8 inch rectangle. Then, cut it into cylinders 3/4 inch wide, about the width of a finger. Roll each piece to about 24 inches long and cut it into 3 8-inch pieces. Twist or braid the pieces together tightly; shape them into a circle and press ends together tightly. Put them on an oiled or
parchment-lined baking sheet. Cover with a towel and let rise another 1 1/4 hours.

Brush taralli with egg whites and bake at 375 F. for 20 minutes. Cool on racks.

One variation: Boil in a lot of water. Scoop them as they come to the surface and put on oiled baking sheet. Bake about 15 minutes. (These would be more bagel-ly)

Another variation: Use 1 1/4 cups water and 1/2 cup lard or olive oil and substitute 2 tsp. pepper for fennel seeds.

This will make about 24 wreaths. Best the day they are made.

Taralli (Cookies)
Source: Gladys Dinletir
Yield: 24 servings

6 eggs; slightly beaten
1/4 lb butter; melted and cooled
1 cup sugar
1/2 cup milk
1 tsp vanilla
6 tsp baking powder
5 cups flour; approximately

Icing:
2 cups confectioner's sugar
4 tsp water; more or less
1 tsp vanilla
colored sprinkles; optional

Place the beaten eggs in a large bowl. Add the butter and sugar gradually, mixing continuously with a wooden spoon.

Add the milk, vanilla, and baking powder, and enough flour to make a firm but soft dough.

Flour your hands. Break off a small piece of dough and roll it into a sausage shape about a 1/2 inch in diameter. Shape it into a ring, joining the ends firmly.

Bake on a greased cookie sheet at 375 degrees for 15 minutes. Set on a rack to cool.

ICING:
Combine the sugar, water, and vanilla in a mixing bowl. Dip the cooled taralli into the icing, or spread the icing over them with your fingers. Top with sprinkles.