Preheat your oven to 350°F (175°C). Line a 9x13 inch baking pan with parchment paper, leaving an overhang on the sides to easily lift the bars out later. Lightly grease the parchment paper.

In a medium bowl, whisk together the all-purpose flour, old-fashioned rolled oats, baking soda, ground cinnamon, ground nutmeg, and salt. Set aside.

In a large mixing bowl, using an electric mixer, cream together the softened unsalted butter, packed light brown sugar, and granulated sugar until light and fluffy, about 2-3 minutes.

Add the large eggs one at a time, beating well after each addition. Stir in the vanilla extract.

Gradually add the dry ingredient mixture to the wet ingredients, mixing on low speed until just combined. Be careful not to overmix.

Press the cookie dough evenly into the prepared 9x13 inch baking pan. Use a rubber spatula or your hands (lightly floured if sticky) to ensure an even layer.

Bake for 25-30 minutes, or until the edges are golden brown and a wooden skewer inserted into the center comes out with moist crumbs, but not wet batter. The center might still look slightly soft, but it will set as it cools.

Remove the pan from the oven and let the bars cool completely in the pan on a wire rack before icing. This is crucial for the icing to set properly.

In a medium bowl, whisk together the powdered sugar, 3 tablespoons of milk (or cream), and vanilla extract until smooth. If the icing is too thick, add more milk, 1 teaspoon at a time, until it reaches a spreadable consistency.

Once the oatmeal bars are completely cool, pour the icing over the top and spread it evenly with a spatula or the back of a spoon.

Allow the icing to set for at least 30 minutes at room temperature, or in the refrigerator for 15 minutes, before lifting the bars out of the pan using the parchment paper overhang.

Cut into 24 squares or rectangles and serve.