Preheat oven to 350°F (175°C). Line an 8x8-inch square baking pan with parchment paper, leaving an overhang for easy removal.

Make the puree: In a small saucepan, simmer raspberries, 2 tbsp sugar, and lemon juice until soft. Press through a fine-mesh sieve to remove seeds. Let the smooth puree cool.

Make the brownie batter: Whisk melted butter and 1 cup sugar. Add 2 eggs one at a time, whisking well. Stir in 1 tsp vanilla. Fold in cocoa powder, flour, and salt until just combined. Spread evenly in the prepared pan.

Make the cheesecake batter: Use a hand mixer to beat softened cream cheese and 1/3 cup sugar until smooth. Beat in 1 egg and 1/2 tsp vanilla just until incorporated. Pour over the brownie batter and spread into an even layer.

Dollop the cooled raspberry puree over the cheesecake layer. Use a skewer or butter knife to gently swirl the puree through the cheesecake and top of the brownie layer.

Bake for 30-35 minutes until the edges are set and the center is slightly jiggly but no longer wet. Cool completely on a wire rack.

Chill the pan in the refrigerator for at least 4 hours, preferably overnight, until very firm.

Use the parchment paper to lift the brownies out of the pan. Use a metal heart-shaped cookie cutter to cut out the brownies, wiping the cutter perfectly clean between each cut. Serve chilled.