3large Honeycrisp apples (about 1 ½ lbs), peeled and grated
½ cup packed light brown sugar
¼ cup heavy cream
¼ cup salted butter
1¼ cups (about 5 oz) powdered sugar, sifted
Prepare the Cream Cheese Filling: Preheat oven to 350°F. Beat cream cheese, 1/4 cup granulated sugar, 1 egg, 2 tablespoons flour, and 1 teaspoon vanilla with an electric mixer on medium speed until smooth.
Prepare the Apple-Spice Batter: Beat brown sugar, oil, and 1/2 cup granulated sugar with an electric stand mixer on medium speed until well blended. Add 3 eggs, 1 at a time, beating well after each addition. Stir in 2 teaspoons vanilla. Whisk together baking powder, pumpkin pie spice, cardamom, salt, baking soda, coriander, and 3 cups flour. Gradually add to brown sugar mixture, beating on low speed until just blended. Add apples, and beat on low speed just until combined.
Spoon half of the batter into a greased and floured 14-cup Bundt pan. Dollop Cream Cheese Filling over the apple mixture, leaving a 1-inch border around edges of pan. Spoon remaining batter over filling.
Bake in preheated oven until a long wooden pick inserted in center comes out clean, 50 minutes to 1 hour. Cool cake in pan on a wire rack 20 minutes; remove from pan to wire rack, and cool completely (about 2 hours). Spoon frosting immediately over cooled cake; sprinkle with pistachios.
Bring brown sugar, cream, and butter to a boil in a 2-quart heavy saucepan over medium, whisking constantly; boil, whisking constantly, 1 minute.
Remove pan from heat; stir in vanilla. Gradually whisk in powdered sugar until smooth. Gently stir until mixture begins to cool and thicken, 4 to 5 minutes. Use immediately.