Begin by crushing your chocolate cookies in a food processor until they achieve a fine crumb consistency. Melt your vegan butter and mix it with the crushed cookies until well combined. Press this mixture firmly into the bottom of a springform pan and chill.

In a small saucepan, heat the vegan heavy cream or coconut cream until it simmers. Remove from heat and pour it over chopped chocolate, letting it sit. Stir until smooth and glossy.

In a large bowl, combine vegan cream cheese, granulated sugar, light brown sugar, cornstarch, and vanilla extract. Beat until smooth. Gradually add the ganache until thoroughly combined.

Pour the cheesecake batter into the chilled cookie crust and smooth the top. Cover with plastic wrap and refrigerate for at least 4 hours.

In a saucepan, combine granulated sugar, light brown sugar, coconut milk, cornstarch, and vanilla extract. Cook while stirring until it thickens. Fold in toasted pecans and shredded coconut.

Spread the coconut pecan topping over the cheesecake and chill for an additional 15-30 minutes before slicing and serving.