For the cookies:
1 1/2 cups rolled oats (not instant)
3/4 cup all-purpose flour
3/4 teaspoon ground cinnamon
1/2 teaspoon baking powder
1/4 teaspoon fine salt
8 tablespoons (1 stick) unsalted butter, at room temperature
1/3 cup packed dark brown sugar
1/4 cup granulated sugar
1 tablespoon molasses (not blackstrap)
1 large egg
1/2 teaspoon vanilla extract

For the filling:
2/3 cup powdered sugar, sifted
3 tablespoons unsalted butter, at room temperature
1 tablespoon heavy cream
1/4 teaspoon vanilla extract
Pinch fine salt