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For brownies: Preheat oven to 350 degrees.
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Lightly grease a 9-inch springform pan.
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In a medium saucepan over low heat, melt butter and chocolate, stirring occasionally.
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Whisk in sugars, salt, and extracts thoroughly, then remove pan from heat.
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Whisk in eggs one at a time, beating well after each addition.
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Stir in flour and cocoa powder just until combined; do not overmix.
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Scrape batter into prepared pan and bake for 30-35 minutes or until a toothpick inserted in the center comes out with moist crumbs but not coated in batter; do not overbake.
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Cool brownies completely on a wire rack.
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For the peppermint frosting: In a medium bowl, beat together 1 cup of powdered sugar and butter with an electric mixer until smooth and well-blended.
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Slowly incorporate another 1/2 cup of powdered sugar; add the milk and peppermint extract and mix until smooth, about a minute.
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Frosting should be spreadable, but thick enough to support the chocolate frosting; add additional powdered sugar a tablespoon at a time if needed to reach appropriate consistency.
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Spread buttercream over cooled brownies.
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For the chocolate frosting: In a small saucepan, bring milk and butter to a boil.
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Place both the chocolates in a medium bowl; once the milk and butter mixture have come to a boil, pour over the chopped chocolate and let sit for about 5 minutes.
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Add vanilla extract to chocolate mixture and whisk until smooth.
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Using an electric mixer, beat powdered sugar into chocolate mixture until smooth.
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Spread frosting over peppermint buttercream frosting.
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Refrigerate torte for at least an hour before serving to allow the frosting to set.
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Torte will keep in the fridge for 5 days, covered.