Preheat oven to 325 degrees F (165 degrees C). Line a 9-inch springform tin with parchment paper.
Combine chocolate wafers and butter in a food processor; process into fine crumbs. Press crumbs evenly into the bottom of the tin. Transfer crust to the refrigerator.
Combine 1 cup heavy cream and basil in a food processor; blend until smooth. Add cream cheese, eggs, 3/4 cup sugar, flour, and cornstarch. Blend until smooth. Pour over chilled crust, smoothing the top with a spatula.
Bake in the preheated oven until surface is firm except for a small spot in the center that will jiggle when the tin is gently shaken, about 1 hour. Turn off oven and open the door. Leave cheesecake in the oven until completely cooled, about 1 hour.
Refrigerate cheesecake until completely set, about 6 hours.
Combine gelatin and water in a small bowl; let stand until softened, 3 to 5 minutes.
Place strawberries in a blender; blend until smooth and frothy.
Pour 1/3 of the strawberries in a saucepan over medium heat; add 1/4 cup sugar. Stir until sugar dissolves, about 3 minutes. Remove from heat and stir in gelatin mixture. Mix in remaining strawberries.
Whip 3/4 cup plus 2 tablespoons heavy cream with an electric mixer until stiff peaks form. Fold in strawberry mixture to make mousse.
Run a knife around the edges of the tin to remove cheesecake; place on a serving platter. Cover top and sides with mousse. Refrigerate until mousse is set, 2 to 3 hours.
