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 egg and vanilla extract and mix until smooth.
Add in the flour mixture and mix until it is fully combined. Add in food coloring and roll cookie dough into balls and flatten slightly. Place one Oreo cookie on each cookie dough and roll into balls. Place onto a large ungreased baking sheet and bake for 10-12 minutes.