Heat oven to 325°F. Line 9 x 9 x 2-inch-square baking pan with regular or nonstick foil.
In food processor, process flour, sugar and butter until mixture looks sandy and begins to clump. Turn into pan; press over bottom. Prick all over with fork.
Bake in 325°F oven 5 minutes. Lower heat to 300°F; bake 30 to 40 minutes or until crust is pale gold. Let cool completely in pan on wire rack.
In large microwave-safe bowl, melt butter on 100% power, 1 to 2 minutes. Whisk in condensed milk and corn syrup. Microwave on 50% power 10 minutes or until boiling; remove from oven every few minutes to stir. Mixture should be thickened and light golden brown. Let stand 1 to 2 minutes. Whisk. Stir in peanuts. Spread over cooled shortbread mixture.
In large microwave-safe bowl, combine bittersweet and milk chocolates. Microwave on 50% power until melted, 2 to 3 minutes; stir to combine. Spread chocolate over peanut filling. Let cool. Once chocolate is set, with sharp knife, cut into 24 bars.