Preheat oven to 350°F and line baking sheets with parchment paper.
In a large bowl, combine melted butter, dark brown sugar, and granulated sugar.
Add molasses, eggs, and vanilla extract. Mix until well combined.
In a separate bowl, whisk together flour, cornstarch, baking soda, cinnamon, and salt.
Gradually add the dry ingredients to the wet ingredients and mix until just combined.
Fold in the instant oats until evenly distributed.
Scoop dough onto the prepared baking sheets, leaving space between the cookies.
Bake for 9–10 minutes, until the edges are set and the centers are still slightly soft.
Allow cookies to cool for several minutes on the baking sheet before transferring them to a cooling rack.
To make the glaze, whisk confectioners' sugar and vanilla with the milk, adding the milk gradually until the desired consistency is reached.
Allow cookies to cool completely before spreading the glaze over the tops.
Let the glaze set completely before serving or storing.