Preheat the oven to 350 F. In a medium bowl, whisk together flour, salt, and baking soda. In a large bowl, combine butter with sugar until fluffy. Add in egg and vanilla extract, and mix until smooth.
Add in the flour mixture, mix until it is fully combined. Divide the cookie dough into two bowls. Color one half blue and the other half green. Take a piece of both colors of dough, and roll them together in a ball. Flatten slightly, and place one Oreo cookie on the dough.
Roll into a ball, covering the Oreo cookie completely. Place the cookies onto a large ungresaed baking sheet at least 2-inches apart. Bake for 10-12 minutes.