Apple Bread Pudding

Name: Apple Bread Pudding
Ingredients: 8 tbsp. salted butter (1 stick), plus more for the baking dish; 10 c. (1-inch) cubes brioche or challah bread (from a 14-to-16-ounce loaf); 3 apples, peeled and cut into 1/2-inch pieces; 1 c. light brown sugar; 3 tbsp. whiskey (optional); Juice of 1/2 lemon; 2 large eggs plus 1 large egg yolk; 3 c. half-and-half; 3/4 c. granulated sugar; 1 tbsp. vanilla bean paste or vanilla extract; 3/4 tsp. ground cinnamon; 1/2 tsp. kosher salt; 4 tbsp. (½ stick) salted butter; 1/2 c. half-and-half; Pinch of kosher salt