Melt 1 ¼ cups butter and mix with oats, flour, and brown sugar in a large bowl until crumbly.
Press two-thirds of this mixture firmly into a greased 9x13-inch baking pan to form the crust.
Preheat oven to 325ºF (160ºC) and bake crust for 10 minutes; then cool slightly.
In a saucepan, melt ¼ cup butter over medium heat, stir in brown sugar until smooth.
Slowly add milk, vanilla, and flour, stirring constantly; simmer for 3 minutes until thickened and glossy.
Pour warm caramel evenly over the baked crust.
Sprinkle the remaining oat mixture over the caramel for a crumbly topping.
Reduce oven temperature to 300ºF (150ºC) and bake for 20 minutes until set.
Allow bars to cool completely before slicing into squares.