For the cheesecake: Grease a 9-by-13-inch baking dish with cooking spray. Pulse the graham crackers and granulated sugar in the bowl of a food processor until fine crumbs form. Drizzle in all the butter while pulsing until the mixture is wet and comes together. Tightly press into the bottom of a 9-by-13-inch baking dish. Chill until ready to use. Clean out the bowl and set aside to use later.
Combine the gelatin with 1/3 cup warm water in a small microwave-safe bowl and set aside to soften, about 5 minutes. Beat the cream cheese on medium-high speed in the bowl of a stand mixer fitted with a paddle attachment (or in a large bowl if using a hand mixer) until completely smooth, about 1 minute. Scrape down the sides of the bowl. Add the confectioners? sugar, sour cream, lemon juice, vanilla and a pinch of salt and beat on medium-high speed until incorporated and smooth, about 1 minute.
Microwave the gelatin until melted, stirring as needed, about 30 seconds. Add the gelatin to the cream cheese mixture and beat on medium-high speed to combine, about 30 seconds. Pour a third of the mixture on top of the graham cracker crust and smooth out with an offset spatula. Refrigerate until slightly set, about 30 minutes. Evenly divide the remaining batter between 2 medium bowls.
Meanwhile, puree the raspberries in the bowl of a food processor until smooth. Fold the puree into one of the bowls and stir gently until completely combined. Pour on top of the plain batter and smooth with an offset spatula. Refrigerate until slightly set, about 30 minutes.
Clean out the bowl of the food processor and puree the blackberries until smooth. Fold into the remaining batter and stir gently until completely combined. Pour on top of the raspberry batter and smooth with an offset spatula. Refrigerate until all three layers are completely set, about 2 hours.
For the streusel: Meanwhile, melt the butter in a large skillet over medium heat. Stir in the flour, granulated sugar, light brown sugar, pecans and cinnamon and cook, stirring frequently and breaking up the clumps as needed, until the mixture is lightly toasted, 5 to 6 minutes. Spread out onto a baking sheet and break up the crumbles so it resembles granola. Let cool completely, about 1 hour.
Cut the cheesecake into bars and sprinkle with the streusel before serving.
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