Preheat oven to 325°F (163°C). Line 9x9-inch pan with parchment paper, leaving 2-inch overhang on two sides for easy removal.
Mix graham cracker crumbs and sugar, then stir in melted butter until mixture resembles wet sand. Press firmly into pan bottom and bake for 10 minutes, then cool while preparing filling.
Whisk cornstarch and water until smooth. In saucepan over medium heat, combine raspberries, sugar, lemon juice, and cornstarch mixture. Crush berries, bring to boil, and cook 3-4 minutes until thickened. Cool to room temperature, then refrigerate.
Beat cream cheese on medium speed for 2-3 minutes until smooth. Add sugar and beat 1 minute. Add flour, sour cream, and vanilla, mixing on low. Add eggs one at a time, beating just until incorporated.
Pour filling over crust and spread evenly. Spoon half the cooled raspberry topping in dollops over filling, then swirl with knife or toothpick to create marbled effect.
Bake 35-40 minutes until edges are set but center still jiggles slightly. Turn off oven, crack door, and let cool inside for 30 minutes.
Cool completely at room temperature for 1 hour. Spread remaining raspberry topping over surface, cover, and refrigerate at least 4 hours or overnight.
Lift bars from pan using parchment overhang. Cut into 16 squares with sharp knife, wiping blade between cuts for clean edges. Serve chilled.