Preheat the oven to 350 F. Line an 8x8 square pan with parchment paper.
Make the raspberry jam first to allow time to cool. In a saucepan, heat the raspberries, sugar and lemon juice over medium heat. Bring to a boil, stirring occasionally to prevent burning.
Reduce raspberry mixture until it has thickened a bit. Strain mixture through a sieve into a bowl. You should have 1/4-1/3 of a cup of raspberry jam. Place into the refrigerator to chill.
Make the cheesecake batter. Combine the softened cream cheese, egg yolk, sugar and vanilla and mix with a hand mixer or a whisk until smooth. Set aside.
Make the brownie batter. In small bowl, whisk the flour, cocoa powder and salt to combine. Set aside.
In a medium saucepan, over the lowest heat setting, melt the butter with the espresso powder.
Once melted, remove the pan from heat and stir in the chocolate chips until completely melted.
Add in both the granulated and brown sugars and stir until combined. The mixture should now be room temperature.
Add in the eggs, one at a time, stirring just to combine after each addition.
Stir in the vanilla extract.
Stir in the flour mixture until just combined.
Pour the brownie mixture into the pan and spread evenly with a spatula.
Using an ice cream scoop, scoop the cheesecake mixture onto the brownies in nine even spots.
Spoon a teaspoon of the raspberry jam over the cheesecake scoops.
Using a butter knife, create swirls in the batter until the jam and the cheesecake are well distributed. Press a few fresh raspberries into the batter.
Place into preheated oven to bake for 38-45 minutes. This time could be a bit longer, or it could be less. Insert a toothpick into the center to check for doneness. There shouldn't be uncooked cheesecake batter. The edges should be visibly cooked, pale brown and the brownies shouldn't jiggle or look wet.
Once baked, set on wire rack to cool. To speed up the cooling process, pop into the fridge after cooling down from the oven for 15 minutes.
Once cool, cut into even bars and serve.