Best Southern Layered Jam Cake

Name: Best Southern Layered Jam Cake
Prep time: 20 min
Cook time: 26 min
Total time: 46 min
Cuisine: American, Southern
Ingredients: 1 cup butter (unsalted, at room temperature); 1 cup granulated sugar; 2.5 cups all-purpose flour; 1 teaspoon baking soda; ½ teaspoon salt; 1 teaspoon ground cinnamon; 1 teaspoon dried ginger; ⅛ teaspoon ground cloves; 3 large eggs (at room temperature); 1 cup blackberry jam (seedless); 1 cup buttermilk (at room temperature); 4 cups brown sugar (packed); ½ cup butter (real butter, no substitute); 5 ounces whole milk; ⅛ teaspoon salt; ½ teaspoon baking powder; ½ teaspoon vanilla extract; 1 tablespoon heavy cream