Preheat oven to 325°F. Grease and flour a 10-inch bundt pan thoroughly, making sure to coat all decorative grooves.
Whisk together dry ingredients. In a large bowl, combine flour, baking soda, cinnamon, and salt. Set aside.
Beat eggs until foamy. In another large bowl, beat eggs for 2 minutes until light and foamy. Add oil, sugar, and vanilla, mixing until smooth and well combined.
Combine wet and dry ingredients. Gradually add the flour mixture to the egg mixture, mixing just until no flour streaks remain. Do not overmix.
Fold in apples and pecans. Gently fold in the chopped apples and toasted pecans with a rubber spatula until evenly distributed.
Pour batter into pan. Transfer batter to the prepared bundt pan, spreading evenly to fill all grooves.
Bake for 55-65 minutes. Bake until a toothpick inserted in the center comes out clean or with just a few moist crumbs.
Cool in pan. Let cake cool in pan for 10 minutes, then invert onto a wire rack to cool completely.
Make the caramel glaze. In a small saucepan over medium-low heat, melt butter. Stir in brown sugar and milk, bringing to a gentle simmer.
Cook glaze until thickened. Simmer for 8-10 minutes, stirring constantly, until slightly thickened. Remove from heat and stir in vanilla.
Glaze the cake. Let glaze cool for 5 minutes until warm but not hot, then drizzle generously over the cooled cake. Serve once glaze has set slightly.