Preheat your oven to 350°F and line your pan with parchment paper. Combine flour, butter, powdered sugar, cinnamon, and salt until crumbly. Add the egg and mix until a dough forms. Press the dough into your pan, prick with a fork, and bake for about 20–25 minutes, or until lightly golden.
While the crust bakes, whisk together granulated sugar, powdered sugar, eggs, yolk, flour, salt, and carrot juice until smooth. Pour the curd mixture over the hot crust and bake again until just set (the center will jiggle slightly). Let it cool completely, then chill until firm.
For the crumble, melt the butter and mix it with walnuts, oats, brown sugar, cinnamon, and salt. Set aside to cool. For the cheesecake layer, whip the heavy cream until stiff peaks form. In a separate bowl, beat the softened cream cheese with sugar, lemon juice, sour cream, and vanilla until smooth. Gently fold in the whipped cream.
Spread the cheesecake mixture evenly over the chilled curd layer. Cover and refrigerate for at least 6 hours, or overnight, until firm. Before serving, top with the walnut crumble for the perfect finishing touch.