Preheat oven to 350ยบ and line a 9-x-13" pan with foil. Spray foil with cooking spray
Prepare brownie mix according to package directions and pour batter into prepared pan.
Prepare cheesecake mixture: In a large bowl, beat cream cheese and 1/2 cup sugar until fluffy. Add eggs, vanilla, and salt and beat until combined.
Pour cheesecake mixture over brownie batter and set aside.
Make raspberry sauce: In a small saucepan over medium-low heat, combine raspberries, remaining 1 tablespoon sugar, and water. Cook, stirring occasionally, until raspberries are broken down, 8 to 10 minutes. Strain seeds through a fine-mesh strainer.
Dollop raspberry sauce all over cheesecake mixture and swirl with a toothpick or wooden skewer.
Bake until edges are set and center of cheesecake mixture is only slightly jiggly, 35 to 40 minutes.
Let cheesecake brownies cool completely in pan.
Slice and serve.