Stir together first 2 ingredients. Let stand 30 minutes.
Meanwhile, beat eggs and granulated sugar at high speed with an electric mixer 2 to 4 minutes or until thick and pale. Add oil and vanilla, beating at low speed just until blended. Add sweet potato puree, beating just until blended and stopping to scrape down sides as needed.
Preheat oven to 350°. Sift together flour and next 5 ingredients; add to egg mixture alternately with buttermilk, beginning and ending with flour mixture. Beat at low speed just until blended after each addition. Drain raisins, reserving rum. Fold raisins into batter. Spoon batter into 3 lightly greased 12-cup Bundt brownie pans, filling each three-fourths full.
Bake at 350° for 14 to 16 minutes or until a wooden pick inserted in center comes out clean. Cool in pans on lightly greased wire racks 5 minutes. Remove from pans to wire racks.
While cakes are baking, bring brown sugar and next 2 ingredients to a boil in a heavy saucepan over medium-high heat. Boil, stirring constantly, 3 minutes or until mixture begins to thicken to a syrup-like consistency. Remove from heat; stir in reserved rum.
Pierce tops of cakes multiple times using a wooden pick. Dip top halves of cakes in glaze, and hold 1 to 2 seconds (to allow glaze to soak into cakes). Place, glazed sides up, on lightly greased racks. Sprinkle each cake with pecans.
Note: To puree roasted sweet potatoes, peel potatoes as soon as they are slightly cooled. Press pulp through a wire-mesh strainer with the back of a spoon. You'll need to roast about 1 1/2 lb. potatoes for 2 cups puree.