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Preheat oven to 350 degrees F. Line cookie sheet with parchment paper.
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In bowl using hand or stand mixer, beat sugar and butter until creamy.
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Add eggs, vanilla and lemon extract and beat until incorporated.
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In small bowl mix together milk and apple cider vinegar. Let sit for several minutes.
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Add milk mixture to other bowl and mix well.
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Add baking soda and flour and mix until all dry ingredients are well incorporated with wet ones and dough is creamy and slightly sticky.
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Using small cookie scoop, scoop dough onto cookie sheet. Press slightly on each cookie to flat out.
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Bake about 10-12 minutes until edges are slightly browned.
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Cool cookies on wire rack.
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In bowl, using hand mixer, mix together powdered sugar, vanilla, lemon juice, maple syrup and milk for vanilla icing. (Note: Corn syrup gives shine to icing, but it can be substituted with maple syrup, if desired.)
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Take half of vanilla icing and move to new mixing bowl. For chocolate icing, add cocoa powder and 2 tablespoons additional milk. Mix well.
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When cookies are completely cooled, turn them flat side up. Using a knife, lightly trace varying phases of eclipse onto each cookie. Using small offset spatula, butter knife or icing tool, spread vanilla icing on one side of knife mark. Let icing set before icing the dark side with chocolate icing. (Note: You can place in freezer 10 minutes, if desired.)
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Once icing is dry on each cookie, arrange on large platter to display phases of eclipse.
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Store cookies in airtight container for 2 days.