1. Preheat your oven to 400°F (200°C). Position the rack in the center of the oven.

2. **Prepare the Pan:** Grease a 9-inch springform pan lightly with butter. Take two large sheets of parchment paper and press them into the pan, overlapping them so they cover the bottom and extend at least 2 inches above the rim. The paper will be crumpled and pleated—this is part of the rustic Basque look!

3. **Mix Cream Cheese:** In a large bowl (or stand mixer with paddle attachment), beat the softened cream cheese and sugar on medium-low speed until the sugar is completely dissolved and the mixture is silky smooth (about 2-3 minutes). Scrape down the bowl.

4. **Add Eggs:** Add the eggs one at a time, beating on low speed after each addition until just incorporated. Do not overbeat once eggs are added to avoid air bubbles.

5. **Add Liquids:** Pour in the heavy cream and vanilla extract. Add the salt. Mix on low until combined.

6. **Add Flour:** Sift the flour over the batter. Gently fold it in with a spatula or mix on the lowest speed just until disappeared.

7. **Bake:** Pour the batter into the parchment-lined pan. Place the pan on a baking sheet (to catch any potential drips) and bake for 50 to 60 minutes.

8. **Don’t Panic:** The top should be very dark brown (even bordering on black spots), and the cake should rise high (like a soufflé). When you gently shake the pan, the center should still be quite jiggly.

9. **Cool:** Remove from the oven and let it cool in the pan on a wire rack. It will deflate significantly as it cools; this is normal. Let it cool completely to room temperature (about 2-3 hours) before unmolding.

10. For the best texture, serve at room temperature.