In one bowl, whisk together flour, sifted cocoa powder, salt, baking soda, and espresso powder—whisking helps distribute the cocoa and leavening agents evenly for consistent texture. In a separate large bowl, cream together butter, sugar, and brown sugar until light and fluffy, about 2-3 minutes, which incorporates air and creates a tender cookie. Add room temperature eggs one at a time, beating well after each addition, then mix in vanilla and red food coloring until the mixture is evenly tinted.
Add the dry ingredient mixture from Step 1 to the wet ingredients in stages, stirring until just combined after each addition—overmixing develops gluten and can make cookies tough. Mix until no streaks of flour remain but stop as soon as the dough comes together. The dough should be thick and well-colored from the red food coloring.
While the dough rests for a minute, roughly chop the Oreos into approximately 1/2-inch pieces—I find hand-breaking them into varied sizes creates better texture than uniform chunks, since some pieces get crispy while others stay chewy. Fold the chopped Oreos and white chocolate chips into the dough using a spatula or wooden spoon until evenly distributed throughout. Don't overmix at this stage; just ensure the mix-ins are incorporated.
Using a cookie scoop or your hands, shape the dough into 20 balls about the size of golf balls, spacing them about 2 inches apart on parchment-lined baking sheets. Gently press each ball down slightly with the heel of your hand to create a uniform thickness—this helps them bake more evenly. Place the baking sheets in the refrigerator for at least 30 minutes; chilling prevents excessive spreading and helps the cookies hold their shape during baking.
Preheat your oven to 375°F and bake the chilled cookies for 12 minutes, until the edges are set but the centers still look slightly underbaked—they'll continue cooking on the hot pan after removal. Let the cookies cool on the baking sheet for 5 minutes to firm up, then transfer to a wire rack. I like to let them cool completely before serving so the white chocolate has time to set and the Oreo pieces stay distinct from the cake texture.