Place the cubed pumpkin in a steamer basket over boiling water. Steam for 15-20 minutes, or until completely tender and easily pierced with a fork. Transfer the steamed pumpkin to a bowl, discarding any accumulated water in the bottom.

While still hot, mash it thoroughly with a fork or potato masher until smooth.

For an ultra-silky texture, press the mash through a fine-mesh sieve. Let the puree cool completely to room temperature before using.

Preheat your oven to 220°C (425°F). Line a 6-inch round cake pan or springform pan with parchment paper, crinkling the paper so it fits the sides.

In a large bowl, combine the softened cream cheese and sugar. Using a silicone spatula or a hand mixer on low speed, mix until completely smooth, creamy, and free of any lumps.

Add the completely cooled pumpkin puree. Mix until fully and evenly incorporated.

Now, add the room-temperature eggs. This is crucial: add them in 3 to 4 separate additions, mixing thoroughly after each addition until the batter is smooth and homogeneous before adding the next batch.

Pour in the whipping cream and sift in the cornstarch. Mix gently until you have a perfectly smooth, lump-free batter.

Pour about one-third of the batter through a sieve into the prepared pan. This ensures no stray lumps make it into the final cake.

If using the optional chestnuts, scatter the chopped pieces evenly over this first layer of batter.

Carefully sieve the remaining batter over the chestnuts (or directly into the pan if not using them). Gently tap the pan on the counter 2-3 times to release any large air bubbles.

Place the pan on the middle rack of the preheated oven.

Bake at 220°C (425°F) for 30 minutes. The top will become very dark brown—almost charred in spots—and the edges will be set, but the center should still have a pronounced, wobbly jiggle when you gently shake the pan. This jiggle is the key to the runny center. Do not overbake.

Remove the cheesecake from the oven. It will deflate slightly, which is normal. Let it cool completely to room temperature on a wire rack (about 1-2 hours).

Once at room temperature, cover it loosely and transfer it to the refrigerator. Chill for at least 4 hours, but ideally overnight. This extended chilling time is essential for the flavors to meld and for the center to achieve its perfect, creamy, sliceable-yet-soft texture.

Remove the cheesecake from the pan using the parchment paper. Slice with a warm, clean knife for neat portions. Serve cold, and enjoy the contrast of the caramelized top, dense cake, and soft, runny heart.