Preheat the oven to 325°F (160°C) and grease a 9-inch springform pan with butter.

In a medium bowl, combine almond flour, 1/3 cup powdered erythritol, and melted butter. Press the mixture firmly into the bottom of the prepared springform pan.

Bake the crust for 10 minutes until slightly golden, then remove from the oven and let cool completely.

Prepare the blackberry sauce by simmering blackberries, 2 tablespoons water, and 2 tablespoons of sweetener in a small saucepan over medium heat for 10 minutes. Mash the berries, strain through a fine-mesh sieve to remove seeds, and set aside to cool.

In a large bowl, beat softened cream cheese and 3/4 cup sweetener until completely smooth. Mix in sour cream, lemon juice, and vanilla extract.

Add eggs one at a time, mixing on low speed just until each is incorporated. Do not overbeat, as air bubbles cause cracking.

Pour the cheesecake batter over the cooled crust. Drop spoonfuls of the blackberry sauce onto the surface and use a toothpick to create a decorative swirl pattern.

Bake for 55 to 60 minutes until the edges are firm but the center remains slightly jiggly. Turn off the oven and prop the door open slightly, allowing the cheesecake to cool inside for one hour.

Transfer to the refrigerator and chill for at least 6 hours, or preferably overnight, before slicing.