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.
¾ cups raspberries, fresh or frozen, 2 tablespoons granulated sugar, 2 teaspoons lemon juice
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.
1 cup (1 - 8oz block) cream cheese, ¼ cup granulated sugar
Beat in the egg yolk and vanilla until thoroughly combined. Set aside.
1 large egg yolk, 1 teaspoon pure vanilla extract
In small bowl, whisk together the flour, cocoa powder and salt. Set aside.
¾ cup all-purpose flour, 2 tablespoons cocoa powder, ½ teaspoon fine sea salt
In a large bowl melt together the butter, chocolate and espresso powder in 30 second increments, stirring well after each increment, until smooth.
½ cup unsalted butter, ⅔ cup bittersweet chocolate, chopped, ½ teaspoon instant espresso or coffee powder
Whisk in in the granulated sugar and brown sugar.
¾ cup granulated sugar, ¼ cup light brown sugar, packed
Whisk in the eggs one at a time. Whisk in the vanilla.
3 large eggs, 1 teaspoon pure vanilla extract
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.