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Preheat oven to 375 degrees.
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In a small bowl, combine the eggs, oil, water and vanilla, and beat with a fork or whisk until light and well-combined. Set aside.
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In a medium bowl, combine the flour, salt, ginger, and baking powder. Add the egg mixture to dry ingredients and stir with a fork until well incorporated. Knead inside the bowl, using your hands, until the dough feels smooth and looks shiny. Cover the bowl with plastic wrap and let rest for 15 minutes.
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After 15 minutes, roll out small handfuls of dough into long, 1/2-inch wide ropes. Cut each rope into 1/3 inch pieces. Roll each piece of dough into balls and place balls onto ungreased cookie sheets. Bake for 20–22 minutes or until golden brown.
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While the dough is baking, making the honey syrup:
In a large, heavy, 3-quart saucepan, add the honey, sugar, ginger, and orange zest and slowly bring to a boil, stirring occasionally. Reduce heat and simmer for exactly 10 minutes.
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Add the teiglach balls to the honey mixture and stir with a wooden spoon until all the teiglach is well-coated. (If you want to add nuts or candied cherries, add them now.) Spoon into paper muffin or cupcake cups and sprinkle with nonpareils or colored sprinkles if you are using them.