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Preheat oven to 450°F. Line a 10-inch springform pan with two large pieces of parchment paper so that they overlap in the middle, pressing and creasing to fit snugly in pan and leaving at least 2 inches of overhang around all edges. Set aside.
Combine cream cheese and sugar in bowl of a stand mixer fitted with the paddle attachment. Begin beating on low speed and gradually increase speed to high, beating until mixture is smooth and creamy, 4 to 6 minutes, stopping to scrape sides of bowl as needed.
Whisk together heavy whipping cream and flour in a medium bowl until mostly smooth; add to cream cheese mixture. Beat on low just until incorporated.
Add eggs and egg yolk, one at a time, beating on medium-low speed until combined after each addition. Add vanilla extract and beat on low speed until blended.
Pour mixture into prepared pan.
Bake in preheated oven until top is dark brown and center is still very jiggly, about 30 minutes.
Transfer to a wire rack to cool to room temperature, about 3 hours. Chill, uncovered, at least 4 hours or up to 3 days.
When ready to serve, remove sides of pan, and carefully peel back parchment paper. Let stand at room temperature at least 30 minutes or up to 2 hours before serving.