Preheat the oven to 425°F (220°C). Line a 6-inch round pan with parchment paper, pressing it in loosely and letting it overhang the sides — the crinkled paper is part of the Basque cheesecake look.
In a bowl, beat the softened cream cheese and sugar until smooth and creamy, making sure there are no lumps.
Beat in the eggs one at a time, then add the heavy cream and vanilla. Mix just until everything is combined — no overmixing here.
Gently fold in the blueberries, flour, and salt, being careful not to crush the berries too much.
Pour the batter into the prepared pan and bake for about 35 minutes. The top should be deeply golden, almost burnt, while the center is still jiggly when the pan is shaken.
Let the cheesecake cool at room temperature for about an hour, then refrigerate it for at least another hour before slicing. The texture sets up beautifully as it chills.