Separate egg yolks from egg whites and beat each separately. Once yolks are firm, mix yolks with olive oil. Next, place flour mixed with baking soda on a board and make a well. Add yolk mixture and whites a little at a time. Blend well and knead for about 10-15 minutes. Cut a piece of dough and roll into a pencil shape, 1/4" round by 6" long. Form into a circle and pinch the ends. Shape all the dough and place on a cloth covered surface. Bring a large pot of water to a slow boil. Drop a few Taralli in the water at a time. (Do not crowd). Remove immediately as they surface. Place on a cloth and let dry 1 to 2 hours. Preheat oven to 500 degrees. Place Taralli on a cookie sheet and bake 20 minutes until they have raised and are golden in color.
Mix confectioners sugar, lemon juice and some water to form an icing. Frost Taralli while still warm.