Toast the walnuts: Dry-roast the California walnuts in 1 tbsp ghee for 3-5 minutes, until lightly browned. Set aside.
Make the carrot halwa layer: Saute the grated carrots in ghee. Add the milk and cook for 10-12 minutes, or until all the moisture has evaporated. Add the sugar and cardamom. The carrots will release more moisture, so continue cooking for another 6 minutes, or until the mixture is dry. Stir in 5 tablespoons of chopped California walnuts. Mix and turn off the stove.
Make the whipped cream: In a large bowl, combine the cold heavy cream, cardamom powder, rose water, and vanilla extract. Using an electric mixer, beat until stiff peaks form. This entire process will take about 5 minutes.
Prepare the mascarpone layer: In a separate bowl, whisk the room-temperature mascarpone for about 10 seconds, just until smooth. Be careful not to overmix, as the mascarpone can become grainy. Gently fold in the whipped cream in batches until combined. Set aside.
Prepare the soaking mixture: Combine all the soaking ingredients (evaporated milk, cardamom, and rose water) in a shallow bowl and mix well.
Assemble the tiramisu: Quickly dip each ladyfinger into the milk mixture for less than a second. Arrange a layer of dipped ladyfingers in your serving dish. Spread a thin layer of the mascarpone mixture on top, followed by a generous layer of carrot halwa (about 5 mini scoops). Add another layer of the mascarpone mixture.
Garnish: Top with a little more carrot halwa, chopped California walnuts, and edible rose petals.
Chill: Refrigerate for at least 6 hours, or preferably overnight, to allow the flavors to meld. Enjoy!