Preheat the oven to 350 F. In a medium bowl, whisk together flour, pudding mix, salt, and baking soda. In a large bowl, mix together butter and sugar until fluffy. Add in the egg and vanilla extract and mix until smooth.
Add in the flour mixture and mix until it is fully combined. Divide the cookie dough between two bowls, mix one with red food coloring and one with green. Take a small amount of each cookie dough and roll together into balls.
Flatten slightly, and place one Oreo cookie in each cookie dough. Roll into balls and place onto a large ungreased baking sheet at least 2-inches apart. Bake for 10-12 minutes.
