Lightly grease a 9-inch square baking pan with butter or vegetable oil, or line the bottom with parchment paper.
Make the filling:
Place the cream cheese, sugar, and sour cream in a medium-size bowl and beat on medium-high speed until blended, 30 seconds.
Scrape the bowl with a rubber spatula.
Add the egg yolks and mix until blended, 20 seconds, set aside.
Prepare the brownie batter:
Melt the chocolate and butter together inches.
the top of a double boiler placed over simmering water.
Remove the chocolate mixture from the heat and let it cool for 5 minutes.
Place the sugar in a medium-size bowl, and pour in the chocolate mixture.
Using an electric mixer on medium speed, mix until blended, about 25 seconds,scrape the bowl.
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.
Then scrape the bowl and blend until velvety, about 15 seconds.
Add the flour on low speed and mix for 20 seconds.
Finish the mixing with a rubber spatula, being certain to incorporate any flour at the bottom of the bowl.
Pour half of the batter into the prepared pan, and spread it evenly.
Using a rubber spatula, scoop the cream cheese mixture onto the brownie batter and gently spread it evenly over the surface.
Distribute the cherries over the filling, and use your fingers to press them down gently into the cream cheese.
Drop the rest of the batter over the filling by large spoonfuls.
Then, using a spatula, spread it as gently as possible over the surface (do not worry if the cream cheese shows in places).
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.
Allow the brownies to cool for 30 minutes in the pan.
Then cut them into 2 1/4-inch squares with a sharp thin knife.
Refrigerate the bars in the pan, covered with plastic wrap, for up to 2 days.
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.
They are delicious either cold or at room temperature.