Heat oven to 350°F. Spray bottom and sides of 13x9-inch pan with baking spray with flour.
In large bowl, beat brown sugar, oil, vanilla and eggs with electric mixer on medium speed until creamy. On low speed, beat in flour, baking soda, pumpkin pie spice and salt until mixed. Add buttermilk; beat on low speed until mixed. Beat on medium speed 1 minute longer. Stir in squash, cranberries and hazelnuts. Pour into pan.
Bake 45 to 55 minutes or until toothpick inserted in center comes out clean. Cool completely, about 1 hour.
In medium bowl, beat butter and cream cheese on medium speed until creamy. Add rum and powdered sugar; beat on low speed until mixed. Beat on medium speed until smooth and creamy. Frost cake. Sprinkle with 1/4 cup hazelnuts. Store covered in refrigerator.