Beat together butter and sugar until light and fluffy.
Blend in egg and vanilla.
Add combined flour, soda, and salt; mix well.
Stir in oats.
Press half of mixture on to bottom of greased 9x13 baking pan. Reserve remaining mixture for topping.
For filling, melt together condensed milk, butterscotch pieces, peanut butter and salt in heavy sauce pan over low heat until smooth. Stir in vanilla.
Spread filling over crust in pan. Sprinkle reserved mixture evenly over filling; press down slightly.
Bake in preheated oven at 350 degrees for 35-40 minutes.