Preheat oven to 350°F
In the bowl of a stand mixer fitted with the paddle attachment, combine granulated sugar, oil, eggs, melted butter, ⅓ cup (73 grams) brown sugar, and 1 tablespoon (13 grams) vanilla; beat at medium-low speed until well combined, about 2 minutes, stopping to scrape sides of bowl.
In a medium bowl, whisk together 3 cups (426g ) flour, 1¾ teaspoons (5.25g ) salt, cinnamon, baking soda, nutmeg, allspice, and cardamom. With mixer on low speed, gradually add flour mixture to sugar mixture, beating until combined and stopping to scrape sides of bowl. (Batter will be quite thick.)
In a medium bowl, stir together apples, pecans, and remaining 2 tablespoons (16g) flour. Fold apple mixture into batter.
Spray a 15-cup Nordic Ware Anniversary Bundt Pan with baking spray with flour. Spoon batter into prepared pan; tap pan on counter several times to evenly spread batter and release any air bubbles.
Bake until a wooden pick inserted near center comes out clean, 50 minutes to 1 hour, rotating pan halfway through baking and loosely covering with foil to prevent excess browning, if necessary.
Meanwhile, in a medium saucepan, combine softened butter, cream, remaining 1 cup (220g) brown sugar, and remaining ½ teaspoon (1.5g) salt. Bring to a boil over medium-high heat, stirring frequently; cook, stirring constantly, for 2 minutes. Remove from heat; stir in rum and remaining 1 teaspoon (4 grams) vanilla.
Remove cake from oven, and poke all over with a wooden pick; pour ¾ cup drizzle(about 195g ) mixture over top, spreading evenly with a small offset spatula. Let cake cool completely in pan on a wire rack. Transfer remaining drizzle mixture to a small microwave-safe bowl, cover, and refrigerate.
When ready to serve, using a small offset spatula, gently loosen cake from center and edges of pan. Remove cake from pan, and place, flat side up, on a serving plate.
Heat remaining drizzle mixture on high in 10-second intervals, stirring between each, until melted and smooth. Using a large spoon, pour drizzle mixture over top of cooled cake, smoothing and spreading as needed. Garnish with pecans, if desired.