Make the Crust:
Line an 8-inch (20 cm) springform or loose-bottom cake pan with parchment paper.
Add the cookies to a food processor and pulse until fine crumbs form. Add the melted butter and pulse until combined. Firmly press the mixture into the bottom of your prepared cake pan. Set aside.
Make the Cheesecake Filling:
Add the vegan cream cheese, sugar, coconut oil, lemon juice/zest, and vanilla extract to a food processor or blender. Blend until smooth and set aside.
In a medium pot over high heat, add the strawberries and a dash of water. Simmer and mash the strawberries until mostly broken down. Cook for 10-15 minutes or until the mixture reduces to about 1/2 heaped cup (~180g). The consistency should be similar to thick tomato pasta sauce.
Add the coconut cream and cornstarch to the pot with the strawberry reduction. Whisk thoroughly. Bring to a gentle boil for 5 minutes, or until the mixture thickens. Don’t worry if the mixture separates!
Add the strawberry mixture to your food processor with the cream cheese mixture. Process until as smooth as possible. If desired, add beetroot powder for color. Taste the mixture and adjust the lemon juice or vanilla as needed.
Pour the cheesecake filling into the prepared cake pan and smooth the top. Cover the pan and chill in the fridge for 4 hours or until set.
Make the Strawberry Topping:
Add the majority of the strawberries and the cornstarch to a small saucepan over high heat. Mash the strawberries with a fork or stick blender. Stir until the strawberries turn into a thick sauce. Sweeten the sauce to taste, if desired. Allow the compote to cool completely.
Just before serving, top the cheesecake with the strawberry compote and reserved fresh strawberries. Store leftovers in the fridge for up to 5 days.