Place the sugar, flour, cornstarch and salt in a small pot and whisk to combine.

Gradually whisk in the milk, taking care to whisk out any lumps.

Place over medium-low heat and cook, stirring often, until thickened.

Pass the mixture through a fine mesh strainer, and into a heat-safe container.

Refrigerate for 2 hours or overnight.

Place the cooled mixture in a large mixing bowl, along with the lemon juice and vanilla, and whip on medium-high speed.

Whip in the cold cream cheese, a tablespoon at a time, allowing each addition to fully incorporate before adding the next.

Whip in the softened butter, a tablespoon at a time, allowing each addition to fully incorporate before adding the next.

Turn the mixer up to high speed, and continue to whip until doubled in volume and very fluffy.