To prepare the bars:
Preheat oven to 350 degrees.
In a medium bowl, whisk together flour, baking soda and salt.
In a large mixing bowl, beat together butter, peanut butter and brown sugar until smooth and well combined. Mix in egg yolks, one at a time, mixing until combined after each. Mix in water and vanilla. Add dry ingredients and stir just until combined. Fold in butterscotch chips.
Scoop mixture into a 9" x 13" baking pan coated with nonstick spray, spreading the dough to evenly cover the bottom with a spatula or your fingertips.
To prepare the topping:
In a clean, large mixing bowl, beat egg whites, cream of tartar and salt with the whisk attachment until they are foamy and begin to thicken. Gradually mix in the brown sugar and continue whipping until the meringue is thick and glossy. Scoop mixture onto the bar batter, spreading smooth with an offset spatula.
Place pan into the oven and bake until the bars are golden brown, about 40 to 45 minutes. Remove from the oven and place pan on a wire rack to cool completely before cutting into bars.