Preheat the oven to 350°F. Line an 8-inch square baking pan with parchment paper, leaving an overhang on two sides for easy lifting. Set aside.
Prepare the raspberry sauce: In a small saucepan, combine the raspberries, 1 tablespoon granulated sugar, and 1 teaspoon vanilla bean paste. Cook over medium heat, stirring occasionally, for 5 to 8 minutes until the berries break down and the mixture thickens and bubbles.
Strain the raspberry mixture through a fine-mesh sieve into a small bowl, pressing to remove the seeds. Discard the seeds and let the sauce cool to room temperature while you prepare the other layers.
Make the cheesecake layer: In a medium bowl, beat the cream cheese and 1/3 cup granulated sugar with a hand mixer until smooth and creamy, scraping down the sides as needed.
Add 1 large egg and 1/2 teaspoon vanilla bean paste to the cream cheese mixture and beat just until fully combined and silky. Set aside.
Prepare the brownie batter: In a medium bowl, whisk together the flour, Dutch-process cocoa powder, and salt until well combined and no streaks remain.
In a large bowl, whisk together the melted coconut oil or neutral oil, 1 1/2 cups granulated sugar, and 1 tablespoon vanilla bean paste until the mixture looks glossy and thick.
Add the 3 large eggs to the oil mixture one at a time, whisking well after each addition until the batter is smooth and shiny.
Add the dry ingredients to the wet ingredients and gently fold with a spatula just until no dry flour remains and the batter is evenly combined. Do not overmix.
Spread the brownie batter evenly into the prepared pan, smoothing the top with a spatula to reach all corners.
Pour the cheesecake mixture evenly over the brownie batter, smoothing it gently to cover the surface in an even layer.
Spoon small dollops of the cooled raspberry sauce over the cheesecake layer, spacing them across the top.
Use the tip of a skewer or a thin knife to gently swirl the raspberry sauce and cheesecake together, making loose figure-eight motions without pushing down into the brownie layer.
Bake the brownies in the preheated oven for 30 to 35 minutes, or until the edges are set, the center only jiggles slightly, and a toothpick inserted into the brownie portion comes out with moist crumbs but not wet batter.
Transfer the pan to a wire rack and let the brownies cool completely to room temperature in the pan.
Once cooled, cover the pan and chill the brownies in the refrigerator for at least 2 hours until firm.
Use the parchment overhang to lift the chilled brownie slab out of the pan onto a cutting board. Use a heart-shaped cookie cutter to cut out heart brownies, pressing straight down and lifting carefully.
Arrange the heart shaped brownies on a serving platter. Serve chilled or at cool room temperature.