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. Fold in the M&Ms. Roll the cookie dough into balls, and flatten each one slightly. Place one Oreo cookie on each piece of dough, and roll into a ball, covering the Oreo cookies completely.
Place onto a large ungreased baking sheet at least 2-inches apart. Bake for 10-12 minutes.