Begin by preheating the oven following the instructions on the brownie mix. Prepare the brownie batter as directed and set it aside.
Using an electric blender, whip the cream cheese until creamy. Blend in 1/3 cup sugar, 1 eggs, and 1 teaspoon vanilla extract. Set aside.
Puree raspberries, strain if desired, and stir in sugar.
In a 8x8 baking dish, coated with oil or lined with parchment paper, spread the brownie mix evenly, reserving 1/4 cup. Cover it with the cheesecake mixture, reserving 1/4 cup. Drizzle raspberry mixture on top, adding dollops of reserved brownie mix and cheesecake mixture as needed. Swirl with a toothpick for a marbled pattern.
Bake uncovered for 25-30 minutes, then an additional 10-15 minutes covered with foil, until the cheesecake is firm and a toothpick comes out clean.
Allow it to cool and refrigerate for 2 hours or overnight.
Store leftovers in a lightly sealed container in the fridge for 3-5 days.