For the Caramel Sauce:
Melt sugar over medium-high heat in medium saucepan. Gently prod sugar as it melts to promote even cooking. Cook until sugar turns deep amber and add butter all at once, whisking to combine. Be very careful with this addition because butter will cause caramelized sugar to bubble and sputter. Keep whisking until butter incorporates (this make take a minute or two).
Remove pan from heat and gradually pour in heavy cream, whisking constantly. When mixture is smooth, stir in vanilla extract and pinch of salt.
Transfer mixture to bowl and let thicken slightly in refrigerator, about 30 minutes.
For the French Toast:
Slice angel food cake into 8 pieces with serrated knife.
Combine eggs, milk, sugar and vanilla in shallow dish. Whisk until well incorporated. Place non-stick skillet over medium heat. Add 2 tablespoons of butter to pan and swirl until melted.
Quickly dip angel food cake pieces into egg mixture and turn to coat all sides. Cook 2-3 slices of cake at a time, turning to cook on all sides until golden. Add additional butter as needed, but you may not have to use all of the butter.
Place slices on serving platter in upright cake formation. Cover with caramel sauce and sprinkle with chopped pecans. Serve immediately.