1. Preheat oven to 350°.
2. Line an 8-inch square glass or ceramic baking dish with parchment paper. Weigh or lightly spoon flour into a dry measuring cup; level with a knife. Place flour, powdered sugar, and salt in a food processor; pulse 2 times to combine. Add chilled butter, and drizzle with ice water. Pulse 10 times or until mixture resembles coarse meal. Pour the mixture into prepared baking dish (mixture will be crumbly). Press mixture into bottom of dish. Bake at 350° for 23 minutes or until lightly browned. Cool completely. Reduce oven temperature to 325°.
3. Place cherries, 1 tablespoon granulated sugar, and 1 tablespoon water in a small saucepan. Bring to a boil. Reduce heat, and simmer 5 minutes or until cherries are tender. Combine lemon juice and cornstarch in a small bowl, stirring with a whisk. Stir cornstarch mixture into cherry mixture; cook for 1 minute or until thickened. Cool mixture slightly. Spoon the cherry mixture into food processor, and process until smooth. Spoon pureed mixture into a bowl, and set aside.
4. Wipe food processor clean. Place cream cheese and remaining ingredients in food processor; process until smooth. Spoon cream cheese mixture over cooled crust; spread evenly. Dollop cherry mixture over cream cheese mixture, and swirl together with a knife. Bake at 325° for 36 minutes or until set. Cool on a wire rack. Cover and chill at least 3 hours.