In a large bowl mix melted butter and melted dark chocolate mix well. Into that add brown sugar, thick Yogurt, and pure vanilla extract. Mix well. Do not over mix.
In the same bowl sieve All-Purpose Flour, Cocoa Powder, and Baking Soda. Mix them with a balloon whisk and sieve it into your bowl containing the wet ingredients. Fold in the wet ingredients with dry ingredients until well combined with a spatula.
Add pitted cherries and mix until combines. Do not over mix.
In another clean and dry medium-sized bowl take cream cheese, granulated sugar. Mix with an electric mixer or stand mixer fitted with a paddle attachment at medium to high speed for 3 minutes. Next, add 1 teaspoon vanilla and beat for an additional 1 minute.
In a 9x9 inch square baking dish lined with parchment paper pour the chocolate cherry brownie batter. Save some to swirl later.Sprinkle Chocolate chips and cherries on it. Even it out using offset spatula. Add a spoonful of the cheesecake batter in even rows on the brownie mix and a spoonful of the leftover brownie batter in between each cheesecake drop. Use the top of a knife or a skewer or a toothpick and drag it back and forth to create the swirl. If you do it too much then the marbelized look will become blurred.
Bake at 350F or 180C for 30-35 minutes. Insert a toothpick in the center of the brownie. If it comes out wet then its not baked. If its comes out with few moist crumbs then its perfectly done. And, if it comes out dry then its over done. Allow it too cool over a cooling rack. Then cut into square brownie pieces using a plastic knife. Enjoy with Cherry Chocolate ice cream.