First things first, let's preheat your oven to 400°F (200°C). While the oven is heating up, grab a 9-inch springform pan. Line the pan with two layers of parchment paper. Don’t worry about making it perfect; the rustic look is part of the charm of Basque cheesecake. Just make sure the parchment paper comes up and over the sides of the pan – this will help it bake properly and prevent sticking.
Now, in a large bowl, put in your softened cream cheese and granulated sugar. It's really important that your cream cheese is softened, otherwise, you'll end up with lumps in your cheesecake. Use an electric mixer (hand mixer or stand mixer) to beat the cream cheese and sugar together until it's smooth and creamy.
Crack your eggs into a separate bowl. Add them one at a time to the cream cheese mixture, mixing well after each egg. Make sure each egg is fully incorporated before adding the next one.
Pour in the heavy cream and vanilla extract. Mix again until everything is well combined and the batter is smooth and liquidy.
Sprinkle the all-purpose flour over the wet ingredients. Mix it in gently until just combined. Be careful not to overmix at this stage, just mix until you no longer see any streaks of flour.
Gently fold in the fresh blueberries into the batter. Distribute them evenly throughout the mixture. Be careful not to squish the blueberries too much while folding.
Pour the cheesecake batter into your prepared springform pan. Place the pan in the preheated oven and bake for 50-60 minutes. Keep an eye on it – you want the top to get really dark brown, almost burnt looking. The center might still jiggle a little, and that’s okay.
Once the cheesecake is done baking, take it out of the oven and let it cool completely at room temperature. This can take a couple of hours. Once it's cooled, cover the pan with plastic wrap and refrigerate it for at least 4 hours, or preferably overnight.
When you're ready to serve, carefully remove the sides of the springform pan. Gently peel away the parchment paper. Your Blueberry Basque Cheesecake is ready to be devoured!