Preheat the oven to 400 degrees F (200 degrees C).

Butter a 9-inch cake pan. Cut a sheet of parchment paper large enough to line the inside of the pan with a few extra inches overhang. Butter the paper and press it into the pan, flattening any major creases. Trim away any excess paper from the sides until you have an inch or two of overhang.

Combine cream cheese, sugar, flour, and salt in a bowl; stir and smear together with a spatula until very smooth and creamy.

Add vanilla and 1 egg; whisk to combine. Whisk in remaining eggs, one at a time. Pour in heavy cream and mix until smooth.

Pour batter into the prepared pan. Tap the pan against the counter to burst any excess air bubbles.

Bake in the preheated oven until puffed, very well browned, and nearly burned on the edges, 50 to 55 minutes. Increase oven temperature to 425 degrees F (220 degrees C) for the last 10 minutes.

Let cheesecake cool to room temperature, at least 25 minutes. Lift out onto a plate and peel back parchment paper, using a knife or spatula if needed.