Preheat oven to 350 degrees F. Grease a 9 inch square baking pan.
To prepare Filling: In a heavy pot, melt 2 tablespoons of the butter and chocolate chips. Add the evaporated milk and 1/4 cup of the white sugar. Bring to a rolling boil, stirring constantly. Remove from heat. Stir in nuts and cool.
To prepare cookie base: Cream 1 1/2 cups of the butter and the brown sugar together. Add the vanilla and the egg, and beat until light and fluffy.
Add the flour, baking soda, and 1 3/4 cups of the oats and blend well.
Press 2/3 of this mixture into the bottom of the greased pan. Spread the cooled filling on top of the cookie crust.
Mix the remaining 1/4 cup of oats with the remainder of the cookie base, and crumble over the filling. Bake for 25-30 minutes.