Preheat oven to 350°. Spray an 8-inch square baking pan with nonstick cooking spray. Set pan aside. Whisk together flour, baking powder and salt in a medium bowl. Set aside. Put butter and sugar in the bowl of an electric mixer fitted with the paddle attachment. Mix on medium speed until pale and fluffy, about 3 minutes. Add eggs and vanilla. Mix until combined. Reduce speed to low. Add flour mixture and mix, scraping down sides of the bowl, until well combined. Mix in butterscotch and brittle. Pour batter into prepared pan; spread evenly with a rubber spatula. Sprinkle the pecan pieces evenly over batter. Bake until golden brown, about 40 to 45 minutes. Let cool completely on a wire rack.
To make homemade pecan brittle: Boil sugars, corn syrup, salt and 1/4 cup water over medium heat to 300°. Remove from heat and add butter, baking soda, vanilla and pecan pieces. Pour onto cookie sheet and let cool.