Heat oven to 350F. Line two large baking sheets with parchment paper. Roughly chop the Oreos into quarters and smaller pieces - you want chunks, not crumbs.

In a medium bowl, whisk together flour, cocoa powder, baking soda, and salt until no cocoa lumps remain. Set aside.

In a large bowl with an electric mixer, beat butter, granulated sugar, and brown sugar on medium speed until light and fluffy, about 3 minutes. Scrape down the bowl once or twice - this step matters for the texture.

Beat in the egg until fully combined, then mix in red gel coloring, vanilla, and vinegar. The batter will look like bright red frosting - that's exactly right.

Add the dry ingredients and mix on low just until no flour streaks remain. Fold in the chopped Oreos with a spatula - don't overmix or you'll crush them to dust.

Scoop dough into 1.5-tablespoon balls and place 2 inches apart on prepared sheets. Bake one sheet at a time for 10-12 minutes, until the edges look set but centers are still slightly puffed and soft. They'll look underdone - that's perfect. Cool on the sheet for 5 minutes, then transfer to a wire rack to cool completely.

Beat softened cream cheese until smooth. Add powdered sugar and milk, beating until pourable but thick enough to hold a line. Add milk by the teaspoon if too thick. Drizzle over cooled cookies in zigzags or dip the tops - your call.