Place a rack in middle of oven; preheat to 400°. Brush pan with unsalted butter, then line with 2 overlapping 16x12" sheets of parchment paper, making sure parchment comes at least 2" above top of pan on all sides. Place pan on a rimmed baking sheet.

Beat 2 lb. cream cheese, room temperature, and 1½ cups (300 g) sugar in the bowl of a stand mixer fitted with the paddle attachment on medium-low speed, scraping down sides of the bowl, until very smooth, no lumps remain, and sugar has dissolved, about 2 minutes.

Increase speed to medium and add 6 large eggs, one egg at a time, beating until each egg is incorporated, about 15 seconds, before adding the next. Scrape down sides of bowl, then reduce mixer speed to medium-low. Add 2 cups heavy cream, 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt, and 1 tsp. vanilla extract and beat until combined, about 30 seconds.

Turn off mixer and sift ⅓ cup (42 g) all-purpose flour evenly over cream cheese mixture using a fine-mesh sieve. Beat on low speed until incorporated, about 15 seconds. Scrape down sides of the bowl and continue to beat until batter is very smooth, homogenous, and silky, about 10 seconds.

Pour batter into prepared pan. Bake cheesecake until deeply golden brown on top and still very jiggly in the center, 60–65 minutes.

Let cool slightly, then unmold. Let cool completely. Carefully peel away parchment from sides of cheesecake. Slice into wedges and serve at room temperature, preferably with a glass of sherry alongside.

Basque cheesecake can be made 1 day ahead. Cover and chill. Let cheesecake sit at room temperature for several hours to remove chill before serving.