In a heatproof bowl, melt 4 tablespoons of the butter in the microwave for 20 seconds and pour into a loaf pan. Set aside.
In a 2nd bowl, whisk together eggs, cinnamon, salt, 1⁄2 cup of brown sugar, 2 teaspoons of vanilla extract, and milk. Add the cubed bread and stir to combine. Soak until bread is saturated, about 15 minutes, tossing and pressing occasionally to submerge the bread. Transfer the soaked bread into the prepared loaf pan and press down slightly. Top with pecans. Cover with plastic wrap and refrigerate for at least 3 hours and up to 12 hours.
The next morning, heat the oven to 350°F. Let the chilled casserole stand at room temperature for 20 minutes. Bake until set and browned, about 45 minutes.
Meanwhile, in a small saucepan over medium heat, heat the remaining 2 tablespoons of butter until lightly browned. Add apples and remaining brown sugar; stir for 5 minutes until sugar dissolves. Add remaining teaspoon of vanilla extract, ground cinnamon, ground cloves, and ground cardamom. Add heavy cream and stir to combine. Simmer for approximately 3 to 5 minutes until sauce is slightly thickened.