Pull out cream cheese and allow to come to room temperature (about 30 minutes).
Preheat oven to 400° with a rack in the center. Butter an 8-inch springform pan. Line with two overlapping sheets of parchment paper (this cake is meant to have rough edges, so don't worry too much about smoothing out the sides completely).
In a medium bowl combine eggs, egg yolks, heavy cream, pumpkin purée, salt, and vanilla. Whisk until smooth.
In a large bowl, or the bowl of a stand mixer fitted with paddle attachment, combine sugar, cinnamon, ginger, and nutmeg and mix until evenly combined. Add softened cream cheese and beat together on medium speed until smooth, about 2 minutes. Scrape down the sides of the bowl.
Gradually add pumpkin mixture to cream cheese mixture on medium-low speed until combined. Scrape down the sides of the bowl.
Add flour. Mix again just until smooth and evenly combined.
Pour batter into prepared springform pan. Place springform pan on a sheet pan. Bake on the middle rack of oven until deeply browned on top, about 60-70 minutes. This cheesecake will still be quite wobbly when you remove it from the oven.
Allow to cool for 10 minutes then unmold and transfer to a wire rack (its okay to leave it on the base of the springform pan). Cool completely (at least 1 hour) before removing parchment. Serve cool or at room temperature.