I believe you are describing "Italian Bow Ties" or Nuckadels (or even Wandies) and not Strufoli (honey balls).
Here's my recipe for the Italian Bow Ties:
6 cups flour
6 tsp baking powder
6 eggs
1 1/2 cups sugar
6 tsp. vanilla
6 1/2 shells of oil (use 1/2 of one of the shells from your eggs.)
Roll out dough 1/2 to 1/4 inch thick and cut in strips abt 6 inches long. We use a pastry cutting wheel to cut strips but you can use a knife. Tie strips into a bow by crossing one leg over the other creating a circle than bring one end into the circle and out again. Deep fry these bows, gently placing them into the hot oil with a slotted spoon, when they start to turn golden, drain on a paper towel and place in a bowel and then pour warm honey on them and sprinkle with confectioners sugar.
I usually cut the recipe in half though.
Here's another recipe I've tried and its been passed down from generation to generation and the directions were hand written by my friend's grandmother:
2 lbs All purpose flour
1 level tsp baking powder
1 tsp salt
8 jumbo eggs
1 cup pure olive oil
Take a well with flour on bread board and add baking powder and salt. Break eggs in the well and add oil. Mix eggs and oil with hand until blended. Gradually, very gradually, gather flour until all flour is absorbed. If dough is too dry add another egg until a medium dough is formed, not too dry. Knead dough for a few minutes then cut it in fourths and knead each piece until its smooth. Put a small amount of flour around each piece and place in covered bowel for about an hour to handle easier. Roll out each piece very very thin and cut into bow and rosettes and fry immediately in hot olive oil in frying pan until brown. When compleletly cooled, place in large container and slowly pour slighty warmed honey over each piece and sprinkle with powdered sugar.