Preheat the oven to 180°C. Lightly grease a deep 20 cm non-stick springform tin, or prepare two small silicone cake moulds.
Mix the crushed almond cookies with the melted butter. Press the mixture firmly into the base of the tin using the back of a spoon. Chill for a few minutes while you prepare the filling.
In a large bowl, combine the mascarpone, cottage cheese, honey (or date syrup), cornflour or polenta, ground almonds, eggs, lemon zest and lemon juice. Whisk until smooth and well blended.
Gently fold most of the blackberries into the mixture. Pour the filling over the prepared base.
Place the tin on a baking tray, then scatter the remaining blackberries over the top, pressing them lightly into the mixture.
Bake for about 30 minutes, until lightly golden and almost set. The centre should still wobble slightly and will firm up as it cools.
If using small moulds, bake for around 20 minutes.
Turn off the oven, open the door slightly, and allow the cheesecake to cool gradually inside the oven.
Once cooled, remove from the tin, cover and chill for at least 2 hours before serving.