Preheat oven to 400°F (205°C). Line a 6" round cake pan with 12" square sheet of parchment paper. The paper doesn't have to fit in the pan neatly.
Beat cream cheese and sugar in a bowl with an electric mixer at low speed for a minute until smooth. Add an egg and a yolk and mix until well combined. Scrape down the sides of the bowl. Add heavy cream, salt, and vanilla, and continue beating for 30 seconds. Then add flour, sifting through a mesh strainer, and beat for 30 seconds. At the end, mix the batter by hand with a spatula.
Pour the batter into the prepared pan, and bake in the preheated oven for 40-45 minutes until the top is dark brown. When the pan is shaken, the cake should be jiggly.
Let cool for 15 minutes, and unmold. Chill in the fridge for 3-4 hours.