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Preheat the oven to 325 degrees F.
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Lightly grease a 9-inch square baking pan with butter or vegetable oil, or line the bottom with parchment paper.
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Make the filling:
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Place the cream cheese, sugar, and sour cream in a medium-size bowl and beat on medium-high speed until blended, 30 seconds.
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Scrape the bowl with a rubber spatula.
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Add the egg yolks and mix until blended, 20 seconds, set aside.
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Prepare the brownie batter:
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Melt the chocolate and butter together inches.
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the top of a double boiler placed over simmering water.
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Remove the chocolate mixture from the heat and let it cool for 5 minutes.
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Place the sugar in a medium-size bowl, and pour in the chocolate mixture.
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Using an electric mixer on medium speed, mix until blended, about 25 seconds,scrape the bowl.
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With the mixer on medium-low speed, add the eggs one at a time, blending after each addition until the yolk is broken and dispersed, about 10 seconds.
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Then scrape the bowl and blend until velvety, about 15 seconds.
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Add the flour on low speed and mix for 20 seconds.
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Finish the mixing with a rubber spatula, being certain to incorporate any flour at the bottom of the bowl.
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Pour half of the batter into the prepared pan, and spread it evenly.
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Using a rubber spatula, scoop the cream cheese mixture onto the brownie batter and gently spread it evenly over the surface.
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Distribute the cherries over the filling, and use your fingers to press them down gently into the cream cheese.
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Drop the rest of the batter over the filling by large spoonfuls.
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Then, using a spatula, spread it as gently as possible over the surface (do not worry if the cream cheese shows in places).
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Bake the brownies on the center rack of the oven until a tester inserted in the center comes out clean or with moist crumbs, about 50 minutes.
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Allow the brownies to cool for 30 minutes in the pan.
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Then cut them into 2 1/4-inch squares with a sharp thin knife.
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Refrigerate the bars in the pan, covered with plastic wrap, for up to 2 days.
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After that, layer them in an airtight plastic container, with plastic wrap, parchment, or waxed paper between the layers, and store for another 2 days in the refrigerator or in the freezer for up to 2 weeks.
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They are delicious either cold or at room temperature.