Preheat the oven to 400° and make sure there is a rack right in the center of the oven. Line a 9-inch springform pan with 2 sheets of parchment paper so they overlap in the middle and leave about a 2-inch overhang all around the rim of the pan. You will have to crease and pleat the parchment to get it to fit, but that will help give this cheesecake its signature edge. Place the prepared pan on a baking sheet and set it aside.
In a large bowl, add the cream cheese and sugar. Beat with the paddle attachment on a stand mixer or a hand mixer on medium speed. Scrape down the sides and bottom of the bowl and mix again until smooth and no lumps of cream cheese remain.
Add the eggs one at a time and beat until each is incorporated before adding the next. Scrape down the sides and bottom of the bowl again and mix for 10-15 seconds longer. Add the flour, cream, salt, and vanilla and mix on medium-low until fully combined.
Pour the batter into the prepared pan. Bake for 60-65 minutes, until the top is a deep brown, and the center of the cheesecake is still jiggly. It will puff up significantly in the center, but it will fall as it cools.
Allow to chill for about 30 minutes before removing from the pan. Let cool until room temperature on a cooling rack. Transfer to the fridge and chill uncovered for at least 4 hours before serving.
Let the cheesecake sit at room temperature for at least 30 minutes before peeling off the parchment before serving.