Caramel Ginger Date Cake

Name: Caramel Ginger Date Cake
Cuisine: American
Ingredients: ½ cup sugar; 3 Tbsp unsalted butter, diced & at room temperature; ¼ cup heavy (whipping) cream; ¾ tsp fleur de sel ((or other coarse sea salt)); 1 cup dates, finely chopped ((about 4 oz pitted dates; see note)); 1 tsp baking soda; 1 cup boiling water; 1¼ cups flour; ¼ cup crystallized ginger, finely chopped ((see note)); 2 tsp baking powder; 1 tsp ground ginger; ½ tsp ground cinnamon; ¼ tsp salt; ¼ cup unsalted butter, at room temperature ((½ stick)); ¾ cup sugar; 2 eggs, beaten; ½ cup unsalted butter, at room temperature; 8 oz cream cheese, at room temperature; 1 cup powdered sugar, sifted; 1 tsp vanilla bean paste ((see note))