Bring all ingredients to room temperature. Soften cream cheese gently if needed, and warm eggs by placing them in warm water for a few minutes.
Grease a loaf pan and line it with parchment paper, allowing extra paper to extend above the edges for easy removal.
In a mixing bowl, beat softened cream cheese, granulated sugar (if using), powdered sugar, lemon juice, and vanilla extract until smooth. Mix on low speed to avoid incorporating too much air.
Add eggs one at a time, mixing gently after each addition. Stir in the extra yolk.
Add cornstarch and mix until incorporated.
Slowly stir in heavy cream until the batter is smooth and silky.
Pour the mixture into the prepared loaf pan. Tap lightly to remove air bubbles.
Bake at 440°F for 25–28 minutes, or until the top is deeply browned and the center still slightly jiggly.
Remove from oven and cool at room temperature for about 1 hour.
Refrigerate for at least 6 hours or overnight before slicing.
The signature texture of Loaf Pan Basque Burnt Cheesecake is achieved by high heat and minimal mixing, creating a creamy interior with a caramelized exterior.