For the COOKIES: In a large bowl whisk together the eggs and sugar. Stir in the softened butter and add in the sour cream, mayo and baking soda mixture and whisk together.
Stir together the baking powder and flour then add to the wet mixture and knead together until the dough comes together and resembles a soft playdough-like consistency.
Preheat oven to 350 ° F. Roll dough into heaping teaspoon sized balls and place onto a baking sheet lined with parchment paper. Bake for 15 minutes.
Carve out the bottom centers of the cookies while still warm.
For the CREAM: Beat together the soft butter and cream cheese until smooth. Mix in the dulce de leche and apricot jam. Beat in the cool whip and mix until light and fluffy (about a minute.)
Fill each hollowed out cookie and join every two halves together. Chill until hard enough to handle when decorating (at least 2 hours.)
For the DECOR: Dilute 1/2 cup of milk with each dye. Add enough food coloring to achieve a medium colored orange and red. (I used Wilton Christmas red and 2 drops of Spectrum super red for the red dye and Wilton creamy peach for the orange dye.)
Dip one cookie half into the orange dye and the other half into the red dye, place on paper towels to set. Once finished dipping, dredge into the sugar. (For an extra crystalized coating dredge in sugar twice.) Refrigerate before serving.