For cake: Grease a 10-cup Bundt pan with shortening. Sprinkle pecans in pan, and swirl pan to coat. Leave remaining pecans in bottom of pan.
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, about 1 hour. Let cool in pan for 10 minutes. Invert onto a wire rack, and let cool for 30 minutes.
For drizzle: In a small saucepan, bring brown sugar, butter, half-and-half, and salt to a boil. Remove from heat, and slowly drizzle over warm cake.