Use a 8 X 8 Square Brownie pan with Cooking Spray and flour, or parchment paper
In a medium bowl, whisk together cream cheese, ¼ cup sugar, 1 egg, ¼ cup jam, and 1 teaspoon of vanilla extract until smooth. Set the bowl aside until later.
In a small bowl, whisk the ½ cup of flour with the teaspoon of salt.
In a large bowl, whisk the 2 eggs plus egg yolk, ½ cup of brown sugar and ¾ cup of granulated sugar ¼ cup of oil, and 1 teaspoon of vanilla extract until smooth.
In the microwave using a small bowl, melt the stick of butter for 45 seconds, and add the dark chocolate and stir until melted. If necessary melt for another 30 seconds. Add 1/2 cup of cocoa powder until smooth.
Combine the sugar mixture with the chocolate mixture and blend until smooth.
Add the flour mixture to the large bowl of chocolate batter and fold until all the flour is incorporated.
Pour the brownie mixture into the brownie pan and smooth the top with an offset knife.
Add the cheesecake batter on top of the brownie batter and smooth it with an offset knife.
Stir the strawberry jam in a small bowl until a smooth consistency. Add spoonfuls on top of the cream cheese topping and using a knife or toothpick and swirl around, being careful not to go too deep into the brownie mixture.
Bake for 35 minutes. The edges will have set but the middle will still have a little jiggle.
Notes
It is preferred to use softened Philadelphia Cream Cheese to prevent lumps and get a creamy consistency in the batter.
Always use Large Eggs when baking for more consistent results. Most recipes are based on large 2 oz eggs.
You can use Dark Chocolate Bars or Dark Chocolate Chips