Make the brownies: Preheat the oven to 325˚. Line a 9-by-13-inch baking pan with foil, leaving a 2-inch overhang on all sides; coat with cooking spray. Whisk the flour, cocoa powder, baking powder, baking soda and salt in a medium bowl.
Melt the butter and milk chocolate in a pot over medium-low heat, stirring. Remove from the heat and whisk in both sugars. Whisk in the eggs, one at a time, then the vanilla and milk. Gently whisk in the flour mixture until just combined. Spread the batter in the prepared pan.
Bake until a toothpick inserted into the center comes out with just a few crumbs, about 45 minutes. Transfer to a rack and let cool completely in the pan. Lift out of the pan using the foil overhang.
Meanwhile, make the topping: Combine the gelatin, salt and 1/4 cup water in a stand mixer fitted with a whisk attachment. Let sit 2 minutes. Combine the granulated sugar, corn syrup and 1/4 cup water in a small saucepan. Bring to a boil over medium-high heat and cook, without stirring, until the sugar is dissolved, 1 minute. With the mixer on low speed, slowly pour in the sugar syrup. Gradually increase the speed to high; beat until thick and fluffy, 12 to 14 minutes. Beat in both extracts.
Coat a rubber spatula with cooking spray; spread the topping on the brownies. Sprinkle with peppermint candies and let set, about 2 hours. Cut into pieces using a knife coated with cooking spray.