Preheat the oven to 200 °F. Cut parchment paper into 3 (9-inch) rounds and place on 2 large baking sheets.
Make the cake: In a large bowl, beat the egg whites, sweetener, cream of tartar, and salt with an electric hand mixer on high speed until stiff peaks form, 5 to 7 minutes. Gently stir in the poppyseeds and extract. Divide the meringue mixture between the 3 parchment rounds, spreading each portion into a smooth and even disk, about 1 inch high.
Bake for 3 hours, then turn off the oven and leave the meringue disks inside the oven, letting the residual heat continue to bake them for another 20 minutes. Transfer the meringue disks to a wire rack to cool completely.
Meanwhile make the filling: Put all the filling ingredients in a blender and puree until very smooth. Taste and add more sweetener as needed. Transfer to a bowl, cover, and keep refrigerated while the meringue disks are cooling.
Assemble the cake: Once the meringue disks have cooled completely, peel off the parchment and place one disk on a cake platter. Using a spatula, spread one-third of the filling on the meringue. Top with raspberries along the outside of the meringue. Repeat with remaining meringue disks, filling, and raspberries.
Cut into slices with a very sharp knife, wiping the blade clean after each cut, and serve.