Preheat the oven to 325˚F. Line a muffin pan with paper liners and set aside.
In a small bowl, mix together the crust ingredients until fully combined. Divide the crust ingredients evenly into the bottom of the lined muffin tin.
Bake in the preheated oven for 5-6 minutes, or until golden brown. Allow to cool completely.
Meanwhile, beat together the cream cheese and 1/2 cup sugar in a stand mixer with a paddle attachment until smooth. Add in the egg, vanilla and applesauce, and mix until fully combined.
Divide the cheesecake batter into 6 small bowls. Add in food coloring to each bowl to make red, orange, yellow, green, blue and purple.
Scoop the cheesecake batter evenly into the prepared muffin pans in the order purple, blue, green, yellow, orange and red.
Return to the oven, and bake at 325˚F for 25-30 minutes, or until cooked through. Place in the refrigerator until cooled.