Melt 1 ¼ cups of butter in a microwave-safe bowl until fully melted and glossy. Allow to cool slightly.

Combine melted butter with quick oats, all-purpose flour, and 2 cups of packed brown sugar in a large mixing bowl.

Grease a 9x13 inch pan and press ⅔ of the oat mixture into the bottom, then bake at 325°F for 10 minutes until edges are golden.

Melt ¼ cup of butter in a saucepan, stir in 1 cup of brown sugar and cook until smooth and bubbling.

Whisk in milk and vanilla extract, then add flour and bring to a gentle boil, simmering until thickened.

Pour the warm caramel filling over the cooled oat crust evenly.

Sprinkle the reserved oat mixture over the caramel layer and gently press down.

Bake at 300°F for 20 minutes until topping is golden brown and crisp.

Let cool completely in the pan for at least an hour, then slice into squares or bars.