Preheat oven to 325°F (163°C). Generously grease every ridge and groove of a bundt pan with butter or nonstick baking spray, then dust with flour and tap out the excess.
In a medium bowl, whisk together the flour, baking soda, salt, cinnamon, and nutmeg until evenly distributed with no visible streaks. Set aside.
In a large mixing bowl, combine the vegetable oil and granulated sugar. Whisk or beat on medium speed until smooth and slightly thickened, about 1 to 2 minutes. Add the eggs one at a time, beating well after each addition, then stir in the vanilla extract.
Add the dry flour mixture to the wet mixture in two or three additions, stirring gently between each addition. Mix just until the flour disappears. The batter will be quite thick, almost like cookie dough.
Add the diced apples and chopped pecans to the batter. Use a rubber spatula to fold them in gently, just until evenly distributed. Avoid overmixing to keep the apple pieces intact.
Spoon the thick batter into the prepared bundt pan and spread it out evenly. Gently tap the pan on the counter to release air pockets. Bake for 55 to 65 minutes, or until a toothpick inserted into the center comes out clean. If the top browns too quickly, loosely tent with aluminum foil for the last 15 minutes.
While the cake bakes, combine the brown sugar, butter, and heavy cream in a small saucepan over medium heat. Stir constantly until the butter melts and the sugar dissolves. Bring to a gentle boil, reduce heat, and simmer for 2 to 3 minutes, stirring often. Remove from heat and stir in the vanilla extract and a pinch of salt.
Once the cake comes out of the oven, let it rest in the pan for 10 minutes. Use a skewer or toothpick to poke small holes across the top of the cake while still in the pan. Slowly pour about two thirds of the warm caramel glaze over the cake, letting it seep into the holes and around the edges. Reserve the rest for serving. Let the cake sit in the pan for another 15 to 20 minutes.
Run a thin knife around the edges of the pan to loosen the cake, then invert it onto a cooling rack or serving plate. Let the cake cool for at least 30 minutes before slicing. Drizzle the remaining caramel glaze over the top just before serving.