Melt the butter in a microwave-safe bowl, heating it for about 1-2 minutes until completely liquefied.
Combine the melted butter with oats, flour, and brown sugar in a large mixing bowl. Stir until a crumbly yet sticky mixture forms.
Press two-thirds of the mixture into a greased 9x13 inch pan to form an even crust.
Preheat the oven to 325°F (163°C) and bake the crust for 10 minutes, then cool for a few minutes.
Melt the remaining butter in a saucepan over medium heat, then add brown sugar and mix until smooth and glossy.
Stir in milk, vanilla extract, and flour, mixing continuously to achieve a smooth caramel filling.
Bring the mixture to a gentle boil and let it simmer for 3 minutes, stirring constantly.
Pour the caramel filling evenly over the cooled crust, spreading it out with a spatula.
Sprinkle the reserved crust crumbs over the caramel filling for topping.
Bake at 300°F (149°C) for another 20 minutes. Allow to cool completely in the pan before cutting into bars.