In the bowl of a stand mixer fitted with the paddle attachment, beat the cream cheese, brown sugar, and sugar on medium-high speed until smooth, about 2 minutes. Add in the heavy cream, yogurt, eggs, egg yolk, and vanilla. Beat to combine for 1 minute. Lastly, add in the flour and salt and stir just until combined.
16 ounces cream cheese, ½ cup brown sugar, ½ cup granulated sugar, ⅔ cup heavy cream, ⅓ cup plain yogurt, 3 large eggs, 1 egg yolk, 1½ teaspoons pure vanilla extract, 3 tablespoons flour, ½ teaspoon kosher salt