Preheat oven to 350 degrees F. Generously butter and flour the bundt pan.
Whisk the flour, 1 1/3 cup of the sugar, 1 teaspoon of the pie spice, the baking powder, baking soda, and salt together in a large bowl.
Toss the apples with the remaining 1/4 cup sugar and 1/2 teaspoon pie spice and set aside.
Whisk the eggs and oil together in another bowl. Whisk in the sour cream, orange zest and juice, and vanilla. Pour the egg mixture into the dry ingredients and stir with a wooden spoon just until combined but still a bit lumpy.
Using a slotted spoon, scatter about 1/2 cup of the apples in the bottom of the bundt pan. Put about 1/3 of the batter on top. Repeat, alternating with the remaining apples and batter, ending with the batter.
Bake the cake until it pulls away for the sides of the pan and a skewer inserted into the center of the cake comes out clean, about 1 hour and 15 minutes. Cool 10 minutes and invert onto a rack placed over a baking sheet. Cool. (The cake can be prepared to this point a day ahead.)
To make the caramel: Stir the sugar, corn syrup, and 2 tablespoons water in a small saucepan. Bring to a boil over medium heat and cook, swirling the pan but not stirring, until the sugar is dark amber-colored caramel, about 15 minutes. Pull pan from the heat and carefully pour in the cream (take care it will splatter). Stir in the pecans, vanilla, and salt. Cool until caramel becomes thick and syrupy, then evenly pour over the cake and cool until set.
Cook's Note: We like to bake this cake the day before we serve it so the flavors and texture ripen. If you bake it a day ahead glaze with the caramel the day you plan to serve it.