Oatmeal Cake with Penuche Frosting

Name: Oatmeal Cake with Penuche Frosting
Ingredients: 8 tablespoons (1 stick) unsalted butter, softened; 1 cup sugar; 2 large eggs, room temperature; 1 teaspoon vanilla extract; 1 1/2 cups unbleached flour; 1 cup oats, ground fine in a blender; 1 tablespoon baking powder; 1 teaspoon ground cardamom; 1/2 teaspoon salt; 1 cup milk; 6 tablespoons unsalted butter; 1/2 cup firmly packed light brown sugar; 1 1/2 tablespoons milk; 1 cup confectioners sugar; 1/2 teaspoon vanilla extract; 1/3 cup very finely ground pecans or walnuts