Sticky Toffee Pudding Ice Cream

Name: Sticky Toffee Pudding Ice Cream
Ingredients: For the sticky toffee pudding; 4 ounces pitted dates, coarsely chopped; 1/2 cup water; 1/2 teaspoon baking soda; 8 tablespoons unsalted butter, room temperature, divided; 1 cup packed dark brown sugar, divided; 1 large egg, room temperature; 5 ounces all-purpose flour; 1/4 teaspoon baking powder; 1/8 teaspoon kosher salt; 1 1/4 teaspoons vanilla extract, divided; 1/2 cup heavy cream; To make the ice cream; 2 cups whole milk; 4 teaspoons cornstarch; 3 tablespoons cream cheese, softened; 1 1/4 cups heavy cream; 2/3 cup sugar; 2 tablespoons light corn syrup; 2 teaspoons vanilla extract