Preheat the oven to 350 F. Line an 8x8 square pan with parchment paper.
In a saucepan over medium heat, combine the raspberries, sugar and lemon juice. Bring to a simmer, smashing the berries and stirring occasionally for 5-8 minutes.
Once the mixture has thickened and reduced, push the mixture through a fine mesh sieve. Cool completely.
In the bowl of a stand mixer fitted with the paddle attachment, beat together cream cheese and sugar until smooth and creamy.
Beat in the egg yolk and vanilla until thoroughly combined. Set aside.
In small bowl, whisk together the flour, cocoa powder and salt. Set aside.
In a large bowl melt together the butter, chocolate and espresso powder in 30 second increments, stirring well after each increment, until smooth.
Whisk in the granulated sugar and brown sugar.
Whisk in the eggs one at a time. Whisk in the vanilla.
Stir in the flour mixture, stirring until just combined.
Pour the brownie mixture into the prepared pan. Spread evenly with a spatula.
Spoon dollops of cheesecake mixture onto the brownies.
Spoon dollops of raspberry jam onto the brownies.
With a skewer or butter knife, create swirls in the batter until the jam and the cheesecake are well distributed. Press a few fresh raspberries into the batter.
Bake for 28-30 minutes, or until a toothpick inserted in the center comes out mostly clean with a few moist crumbs. The center should have just a slight jiggle.
Allow the brownies to cool for about 20 minutes on the counter, then place the pan in the fridge and allow to cool for another 2-3 hours prior to serving.