Preheat the oven to 350°F. Grease a 12 by 9 by 2-inch glass baking dish.
Beat together the butter and the granulated sugar until soft and creamy. Blend in the brown sugar, and then the peanut butter. Add the salt, vanilla, and eggs and beat until light and fluffy. Blend in the flour.
Spread the batter evenly in the prepared pan. Bake for 30 to 35 minutes, or until golden brown on top.
Remove from the oven and immediately sprinkle the chocolate morsels over the top of the brownies. Give them time to melt, and then spread evenly with a spatula. Cool in the pan on a wire rack. When cool, cut into 2-inch squares (4 across, 6 down).
Yield: 24 brownies, each a 2-inch square