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Preheat the oven to 350°F with a rack in the center. Lightly grease an 8" square pan. Line the pan with a parchment sling and lightly grease the parchment.
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To make the peppermint swirl: In a small bowl, whisk the cream cheese, sugar, milk, flour, peppermint oil, and food coloring until well combined, forming a pale green paste.
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For a striped or feathered look, transfer the peppermint swirl topping to a zip-top bag or a piping bag fitted with 1/2" round piping tip. For a simpler finish, simply set the topping aside.
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To make the batter: In a medium bowl or the bowl of a stand mixer fitted with the flat beater, beat the eggs, cocoa, vanilla, and salt to form a thick, uniform paste, scraping the bowl as needed.
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In a large saucepan set over low heat (or in a medium microwave-safe bowl), melt the butter, then add the sugar, and whisk to combine. Continue to heat (or microwave) briefly, just until the mixture is hot but not bubbling (about 110°F to 120°F); it’ll become shiny as you stir. The sugar will not dissolve fully; that’s OK.
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Add the cocoa mixture to the sugar mixture and whisk until well combined.
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Add the flour and whisk until well combined; the batter should be smooth and shiny.
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Transfer the batter to the prepared pan and spread into an even layer. A small offset spatula is a helpful tool here.
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To add the peppermint swirl: If the filling is in a zip-top bag, snip the corner of the bag, creating an opening about 1/2" wide. Using the zip-top bag or piping bag, pipe five to six evenly spaced stripes of filling across the surface of the brownies.
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Use a butter knife or wooden skewer to draw alternating lines perpendicularly through the peppermint stripes, pulling them into a feathered pattern. To Bake It Easy, dollop the mixture on top of the batter and use a butter knife or wooden skewer to swirl it in gently, creating a marbled effect.
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Bake the mint brownies for 28 to 32 minutes, until the edges feel set and a toothpick or the tip of a sharp knife inserted into the center comes out with moist crumbs clinging to it but no raw batter. A digital thermometer inserted in the center should register 205°F when the brownies are done.
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Remove the brownies from the oven and let them cool completely in the pan on a rack. Use the parchment to lift the brownies out of the pan and transfer them to a cutting board before slicing.
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Storage information: Store leftover mint brownies in an airtight container at room temperature for several days; freeze for longer storage.