Prep your pan and oven. Preheat oven to 325°F (165°C). Line an 8x8-inch baking pan with parchment, leaving overhang for easy lifting.
Lightly grease the sides.
Make the crust. In a bowl, mix almond flour, coconut flour, granulated sweetener, and salt. Stir in melted butter and vanilla until it resembles damp sand and clumps when pressed.
Press and par-bake. Press the crust firmly and evenly into the pan. Use a flat-bottomed cup to compress.
Bake for 10–12 minutes until just set and lightly golden at the edges. Set aside to cool slightly.
Beat the filling. In a large bowl, beat softened cream cheese until smooth and fluffy, about 1–2 minutes. Add powdered sweetener and mix until creamy.
Beat in eggs one at a time. Add sour cream, vanilla, lemon zest, and a pinch of salt. Mix just until smooth; don’t overbeat.
Simmer the strawberries. In a small saucepan, combine strawberries, sweetener, and lemon juice.
Cook over medium heat for 5–7 minutes, stirring, until the berries release juices and soften. Mash lightly. Stir in vanilla.
If you want it thicker, sprinkle in xanthan gum and whisk, or stir in chia seeds and let sit a few minutes to gel. Cool slightly.
Assemble. Pour the cream cheese mixture over the warm crust and smooth the top. Spoon small dollops of the strawberry mixture across the surface.
Use a skewer or knife to gently swirl the berries into the cream cheese without overmixing.
Bake to set. Bake at 325°F (165°C) for 22–28 minutes, until the edges are set and the center still has a slight jiggle. Avoid browning the top.
Cool and chill. Let the pan cool on a rack for 1 hour. Then cover and chill at least 4 hours, ideally overnight, to firm up and develop flavor.
Slice and serve. Lift the slab out with the parchment and cut into 16 squares with a sharp knife, wiping between cuts for clean edges.
Serve as is or with a tiny dollop of whipped cream.