Preheat oven to 350°F and line baking sheets with parchment paper.
In a large mixing bowl, cream together the butter, granulated sugar, and brown sugar until light and fluffy, about 3 minutes.
Add the eggs, vanilla extract, peppermint extract, and food coloring (if using), mixing until fully combined.
Add the flour, baking soda, and salt, and mix just until a soft dough forms. Do not overmix.
Scoop about 2 tablespoons of dough, flatten slightly, place one Mint Oreo in the center, and wrap the dough completely around the cookie, sealing all edges. Roll gently into a ball.
Place dough balls on the prepared baking sheets, spacing them about 2½ inches apart.
Bake for 10–12 minutes, until the edges are set and the tops look slightly underbaked.
Allow cookies to cool on the baking sheet for 5 minutes, then transfer to a wire rack to cool completely.