Preheat oven to 325°F. Grease a 10-cup Bundt pan with shortening. Sprinkle pecans into pan, swirling pan while tapping it firmly to coat well with pecans. Remove any loose pecans onto a cutting board; chop finely and return to pan, again swirling and tapping pan to help coat.

In the bowl of a stand mixer fitted with the paddle attachment, beat butter, sugar, and vanilla at medium speed until fluffy, 4 to 5 minutes, stopping to scrape sides of bowl. Add eggs, one at a time, beating well after each addition.

In a medium bowl, whisk together flour and baking powder. In a small bowl, stir together corn syrup and buttermilk. Gradually add flour mixture to butter mixture alternately with buttermilk mixture, beginning and ending with flour mixture, beating just until combined after each addition. Spoon batter into prepared pan.

Bake until a wooden pick inserted near center comes out with a few moist crumbs, 1 hour to 1 hour 10 minutes, loosely covering with foil after 45 minutes of baking. Let cool in pan on a wire rack for 25 minutes. Loosen cake from center of pan using a small offset spatula. Invert cake onto a wire rack. Remove cake from pan, and let cool for 30 minutes.

For drizzle: In a small saucepan, bring brown sugar, butter, heavy cream, and salt to a boil. Reduce heat, and let simmer, uncovered, for 5 minutes. Remove from heat, and slowly drizzle over warm cake.