Preheat oven to 325 degrees, with rack set in lower third. Assemble a 9-inch springform pan with the rimmed side of the pan facing down. Coat pan with cooking spray; line side with a long strip of waxed or parchment paper.
In a food processor, grind graham crackers until fine crumbs form. Add oil, and pulse to moisten. Transfer crumbs to prepared pan, and press firmly into the bottom. Place pan on a rimmed baking sheet; bake until crust is lightly browned, about 15 minutes.
Meanwhile, wipe bowl and blade of food processor. Blend cottage cheese and cream cheese until very smooth and glossy, scraping down bowl as necessary, 4 to 5 minutes. Add 3/4 cup sugar, sour cream, eggs, flour, vanilla, and salt; blend just until filling is smooth.
Pour filling onto crust (crust can be hot or warm). Bake until barely set in center, about 1 hour. Turn oven off; let cake cool in oven 1 hour. Transfer to a wire rack, and let cool to room temperature, about 2 hours. Refrigerate until firm, at least 3 hours and up to 2 days.
Make topping: In a large skillet, combine cherries and remaining 2 tablespoons sugar. Boil over high heat until liquid is thick and syrupy, 10 to 15 minutes. Cool, and refrigerate for at least 2 hours and up to 2 days.
To serve, unmold cheesecake (peel off and discard paper). Transfer to a serving platter; top with cherry topping.