Place a rack in middle of oven; preheat to 200°. Brush pan with unsalted butter, then line with 2 overlapping 16"x12" sheets of parchment paper, making sure parchment comes at least 2" above top of pan on all sides. Because the parchment needs to be pleated and creased in some areas to fit in pan, you won’t end up with a clean, smooth outer edge to the cake; that’s okay! Place pan on a rimmed baking sheet.

Beat cream cheese, room temperature, and 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 the eggs, one 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 the cream, salt and vanilla extract and beat until combined, about 30 seconds.

Turn off mixer and sift 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 (yet again) 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 (cake will collapse drastically as it cools), 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. Do Ahead: 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.