1. Preheat the oven to 325°F (163°C). Wrap the bottom of a 9-inch springform pan in two layers of foil and lightly grease the inside.

2. Mix graham cracker crumbs with brown sugar and melted butter. Press into the bottom of the pan. Bake for 8 minutes. Cool slightly.

3. Beat the softened cream cheese until smooth. Add sugar and mix until incorporated. Blend in sour cream, vanilla, and then the eggs one at a time, mixing gently.

4. Pour the cheesecake layer over the baked crust and refrigerate for 10 minutes to slightly firm up.

5. In a separate bowl, whisk flour, baking soda, cinnamon, nutmeg, and salt. In another bowl, whisk eggs, oil, and sugar. Combine wet and dry ingredients, then fold in grated carrots.

6. Carefully spoon the carrot batter in swirls into the cheesecake layer. Smooth the top gently.

7. Place the pan into a water bath and bake for 60-70 minutes until the center is just set. Turn off oven, crack the door, and cool for 1 hour.

8. Remove from the oven, then refrigerate the cake for at least 4 hours or overnight.

9. For the topping, whisk milk, cornstarch, sugar, and egg yolks in a saucepan. Cook over medium heat until thickened. Remove from heat and stir in butter and vanilla. Cool slightly.

10. Spread topping over the chilled cheesecake and top with toasted nuts.

11. Chill at least 1 hour more before slicing. Serve at room temperature for best texture.