Step 1

For the crust: Position an oven rack in the bottom third of the oven and preheat to 350 degrees F. Spray a 9-inch square baking pan with nonstick cooking spray. Line the bottom of the pan with parchment, leaving a 2-inch overhang on 2 of the sides.

Step 2

Add the flour, confectioners’ sugar, butter, cinnamon and salt to a food processor. Pulse until the mixture resembles coarse meal with some pea-size pieces. Add the egg and 1 tablespoon cold water and pulse until the dough comes together. Press the dough into the bottom of the prepared pan. Prick the dough all over with a fork. Bake until the crust is golden brown, 20 to 25 minutes. Let cool slightly on a rack, about 15 minutes.

Step 3

For the carrot juice curd filling: Meanwhile, whisk the carrot juice, granulated sugar, milk, cinnamon, salt and whole eggs and yolks in a medium saucepan over medium-low heat until well combined. Add the butter a few pieces at a time, whisking constantly and making sure the butter is melted before adding more, and continue to cook until the mixture is thick, a little lighter in color and coats the back of a spoon, 12 to 15 minutes. Strain the curd if any lumps form, then pour into the crust and smooth with a spatula.

Step 4

Bake until the curd is set (a small part in the center may still be a little jiggly), 35 to 40 minutes. Let cool slightly on a rack, about 30 minutes, then transfer to the refrigerator to cool completely, about 30 minutes.

Step 5

For the walnut crumble: Meanwhile, microwave the butter in a small microwave-safe bowl until melted, about 1 minute. Stir in the walnuts, brown sugar, oats, cinnamon and salt. Microwave until the sugar is dissolved, about 1 minute. Let cool in the bowl until the crumble is crunchy, about 30 minutes. Cover tightly or transfer to an airtight container and store at room temperature until ready to use.

Step 6

For the no-bake cheesecake: Once the curd filling is chilled, whip the heavy cream in a medium bowl with a whisk until stiff, fluffy peaks form, 3 to 4 minutes (or 1 to 2 minutes using an electric mixer on medium speed); set aside.

Step 7

Beat the cream cheese and granulated sugar in a stand mixer fitted with the paddle attachment on medium speed, scraping down the sides of the bowl as needed, until light and fluffy, 3 to 4 minutes. Reduce the speed to medium low, add the lemon juice, sour cream and vanilla and beat until just combined, 1 to 2 minutes. Gently fold the whipped cream into the cream cheese mixture with a large rubber spatula.

Step 8

Pour the batter on top of the curd filling and smooth the top with an offset spatula. Cover tightly and refrigerate until set, at least 6 hours and up to 24 hours.

Step 9

Just before serving, sprinkle the walnut crumble on top. Cut into squares and serve cold.