Oatmeal Cake with Penuche Frosting

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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

Penuche frosting:

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