Preheat the oven to 400°F (204°C). Line an 8 x 3-inch round baking pan with two large sheets of parchment paper, allowing plenty of overhang on all sides. Secure with metal binder clips if needed.
In the bowl of a stand mixer fitted with the paddle attachment (or using a hand mixer), beat the cream cheese, sugar, cornstarch, salt, and vanilla extract on low speed until completely smooth and free of lumps, about 2–4 minutes. Scrape down the sides and bottom of the bowl as needed.
With the mixer running on low speed, add the eggs one at a time, allowing each egg to fully incorporate before adding the next, about 30–60 seconds between additions.
Scrape the bowl again. With the mixer on low speed, slowly stream in the heavy whipping cream and mix until the batter is smooth and fully combined.
Pour the batter through a large sieve into the prepared pan to remove any lumps and excess air bubbles. Gently tap the pan on the counter a few times.
Bake for 45 minutes. The cheesecake should be puffed, lightly to deeply browned on top, set around the edges, and slightly jiggly in the center.
For a darker caramelized top, switch the oven to broil during the last 1–2 minutes of baking, watching carefully to prevent burning.
Let the cheesecake cool in the pan at room temperature for at least 2 hours.
Refrigerate for 4–6 additional hours or overnight before slicing and serving.