Preheat oven to 350°F (175°C) and line an 8-inch square pan with parchment paper.
Whisk together flour, sugar, cocoa powder, baking powder, baking soda, and salt in a large bowl.
Add milk, vegetable oil, egg, and vanilla extract to dry ingredients and mix until smooth.
Gently stir in hot water until batter is thin and well combined.
Pour batter into prepared pan and bake for 20–22 minutes until a toothpick comes out clean.
Cool the cake completely in the pan.
Evenly spread chopped chocolate sandwich cookies over the cooled cake and drizzle with peppermint extract.
In a small saucepan, heat sugar and water over medium heat, stirring until sugar dissolves.
Cook sugar syrup without stirring until it turns golden amber, about 4-5 minutes.
Pour hot caramel onto parchment-lined baking sheet; sprinkle with almonds and crushed peppermint candies.
Let caramel cool and harden, then break into shards.
Melt chocolate chips in microwave in 30-second intervals, stirring until smooth.
Drizzle melted chocolate over cookie-topped cake.
Arrange brittle shards upright on the chocolate layer to create a scattered effect.
Refrigerate for 15 minutes to set chocolate before slicing and serving.