Caramel Apple Bread Pudding

Name: Caramel Apple Bread Pudding
Ingredients: Nonstick cooking spray; 6 large eggs; 3 cups half-and-half; 1/2 cup light brown sugar, lightly packed; 1/2 cup granulated sugar; 1 teaspoon vanilla extract; 1/2 teaspoon kosher salt; 1 tablespoon ground cinnamon; 1 teaspoon ground nutmeg; 1/2 teaspoon ground ginger; 1 loaf brioche, cut into 1 1/2-to-2-inch cubes; 1 1/2 cups peeled, cored, small diced Granny Smith apples (from about 1 1/2 apples); Vanilla ice cream, for serving (optional); Store-bought or your favorite homemade caramel sauce