Lightly grease or line an 8-by-8-inch square baking pan with parchment paper, leaving overhang for easy lifting.

In a medium bowl, combine the almond flour, 1/4 cup sugar-free granulated sweetener, melted butter, 1/2 teaspoon vanilla bean paste, and salt.

Mix with a spoon or spatula until the mixture looks like damp sand and holds together when pressed.

Transfer the crust mixture to the prepared pan and press it firmly and evenly into the bottom to form a compact layer.

Place the pan in the refrigerator to chill while you prepare the filling.

In a large mixing bowl, add the softened cream cheese and sugar-free powdered sugar.

Beat with a hand mixer on medium speed until completely smooth and creamy, scraping down the sides of the bowl as needed.

Add the sour cream, 1 teaspoon vanilla bean paste, and lime juice to the cream cheese mixture.

Mix on low speed just until the filling looks silky, smooth, and fully combined.

Taste the filling and adjust sweetness or lime juice if desired, mixing briefly after any additions.

Remove the chilled crust from the refrigerator and pour the cheesecake filling over the crust.

Spread the filling evenly with an offset spatula or the back of a spoon, smoothing the top and pushing it into the corners.

Cover the pan tightly with plastic wrap or foil.

Refrigerate for at least 4 hours, or until the cheesecake bars are completely set and firm to the touch.

Shortly before serving, combine the mixed berries and 1 tablespoon sugar-free granulated sweetener in a small bowl.

Stir the berries and let them sit at room temperature for 10 to 15 minutes until they release some juices.

Once the cheesecake is set, use the parchment overhang to lift the slab from the pan onto a cutting board.

Run a sharp knife under hot water, dry it, then cut the cheesecake into 16 even bars, wiping the knife between cuts.

Spoon the sweetened berries and their juices over the bars just before serving, or serve the topping on the side.