How to Make It
Preheat oven to 350°F. Beat butter with a heavy-duty electric stand mixer on medium speed until creamy. Gradually add sugars, and beat until fluffy. Add eggs, 1 at a time, beating just until blended. Add pumpkin and vanilla, beating just until blended.
Stir together flour, baking powder, pumpkin pie spice, baking soda, and salt. Add to butter mixture alternately with buttermilk, beginning and ending with flour mixture. Beat at low speed just until blended after each addition. Stir in chopped pecans. Spoon batter into a greased (with shortening) and floured 12-cup Bundt pan.
Bake in preheated oven until a wooden pick inserted in center comes out clean, 50 to 60 minutes. Cool in pan on a wire rack 10 minutes; remove from pan, and cool completely on a wire rack, about 1 hour. While cake bakes, prepare Candied Pecans.
Prepare the Candied Pecans: Stir together 1/4 cup granulated sugar, 1/4 tsp. pumpkin pie spice, and a pinch of salt in a heavy saucepan over medium. Add 1 cup roughly chopped pecans, and cook, stirring constantly, until sugar melts and coats pecans, 7 to 8 minutes. (Sugar will appear grainy before it melts and coats pecans.) Spread on lightly greased (with cooking spray) wax paper, and cool 20 minutes.
Prepare the Brown Sugar Icing: Bring 1 cup packed light brown sugar, 1/3 cup heavy cream, and 1/4 cup salted butter to a boil in a 1-quart saucepan over medium, stirring often. Boil, stirring often, 1 minute; remove from heat. Gradually whisk in 1 cup powdered sugar and 1 tsp. vanilla extract until smooth.
Spoon icing over top of cake, allowing it to drip down sides. Top with Candied Pecans while icing is still soft.