Preheat the oven to 325°F. Grease every ridge of a 12-cup bundt pan thoroughly with a butter-and-flour combination or baking spray with flour.
Beat the butter and cream cheese together on medium speed for 2 minutes until smooth. Add the sugar and beat for 3 minutes until light and fluffy.
Add the eggs one at a time, beating just until incorporated after each. Mix in the vanilla extract.
Whisk the flour, baking powder, and salt together in a separate bowl. Add to the batter in three additions on low speed, mixing just until no streaks of flour remain.
In a small bowl, stir together the brown sugar, cinnamon, and flour for the swirl. Stir in the melted butter to form a thick paste.
Spoon half the batter into the prepared pan. Sprinkle the cinnamon swirl mixture evenly over the top. Spoon the remaining batter over the swirl and drag a knife through the layers once in a gentle zigzag.
Bake for 60–70 minutes, until deep golden and a toothpick inserted into the thickest part comes out with a few moist crumbs.
Cool the cake in the pan on a wire rack for exactly 15 minutes, then invert onto the rack and remove the pan.
While the cake bakes or cools, melt the butter for the caramel in a heavy-bottomed saucepan over medium heat. Whisk in the brown sugar and cook for 2 minutes until bubbling.
Slowly whisk in the heavy cream (the mixture may look separated briefly — keep whisking) and simmer for 2–3 minutes until it coats the back of a spoon. Stir in the salt, vanilla, and toasted pecans.
Pour the warm caramel evenly over the cake while it's still resting at the 15-minute mark, letting it drip down the ridges. Let set for 20 minutes before slicing.