Step 1

Position a rack in the bottom third of the oven.

Step 2

Preheat the oven to 350 degrees F.

Step 3

Spray a 9-inch square baking pan with nonstick cooking spray and line the bottom with parchment paper, leaving a 2-inch overhang on two sides of the pan.

Step 4

In the bowl of a food processor, add the flour, the confectioners' sugar, 8 tablespoons of the butter, 1/2 teaspoon of the cinnamon, and 1/4 teaspoon of the salt and pulse until the mixture resembles a coarse meal with some pea-sized pieces.

Step 5

Add the egg and the water to the flour mixture and pulse until the dough comes together.

Step 6

Press the dough into the bottom of the prepared pan and prick it all over with a fork.

Step 7

Bake the dough until the crust is golden-brown, about 20-25 minutes.

Step 8

Transfer the baked crust to a wire rack and allow it to cool for 15 minutes.

Step 9

Heat a medium saucepan over medium-low heat and add the carrot juice, 1/2 cup of the granulated sugar, the milk, 1/2 teaspoon of the cinnamon, 1/4 teaspoon of the salt, the remaining whole eggs, and the egg yolks and whisk together until well combined.

Step 10

Add 1 cup of the butter to the carrot juice mixture, a few pieces at a time, whisking constantly, and making sure the butter is melted before adding more, and cook until it thickens and coats the back of a spoon, about 12-15 minutes.

Step 11

Strain the carrot filling and pour it into the prepared crust and use a spatula to smooth it out.

Step 12

Bake the carrot filling until it sets, about 35-40 minutes.

Step 13

Transfer the carrot filling to a wire rack and allow it to cool slightly, about 30 minutes.

Step 14

Transfer the carrot filling to the refrigerator to cool completely, about 30 minutes.

Step 15

In a small microwave-safe bowl, microwave the remaining butter until melted, about 1 minute.

Step 16

Add the walnuts, the brown sugar, the oats, the remaining cinnamon, and the remaining salt to the butter and stir to combine.

Step 17

Microwave the walnut mixture until the sugar dissolves, about 1 minute.

Step 18

Allow the walnut mixture to cool in the bowl until it is crunchy, about 30 minutes.

Step 19

Transfer the walnut crumble to an airtight container and store at room temperature.

Step 20

In the bowl of a stand mixer fitted with the whisk attachment, whip the heavy cream until stiff, fluffy peaks form, about 3-4 minutes.

Step 21

In the bowl of a stand mixer fitted with the paddle attachment on medium speed, add the cream cheese and the remaining granulated sugar and beat, scraping down the sides of the bowl as needed, until it is light and fluffy, about 3-4 minutes.

Step 22

Adjust the mixer speed to medium-low and add the lemon juice, the sour cream, and the vanilla to the cream cheese mixture and beat until just combined, about 1-2 minutes.

Step 23

Gently fold the whipped cream into the cream cheese mixture with a large rubber spatula.

Step 24

Pour the cream cheese mixture over the top of the carrot filling and smooth the top of the cream cheese mixture with an offset spatula.

Step 25

Cover the cheesecake tightly and refrigerate until it sets, for at least 6 hours and up to 24 hours.

Step 26

Sprinkle the walnut crumble over the top of the cheesecake.

Step 27

Cut the cheesecake into squares.

Step 28

Serve cold.