Preheat oven to 375°F. Butter and flour a 13x9x2-inch baking pan; set aside.
Melt the butter in a large microwave-safe bowl. Stir the sugar into the butter until smooth; cool to room temperature. In another medium bowl whisk the flour, baking soda, and salt together. Beat the eggs and vanilla into the sugar mixture. Add the flour mixture a bit at a time and mix until a smooth thick batter forms. Fold in the chocolate pieces. Spoon the batter into the prepared pan and spread evenly.
Bake until the blondies are light brown, about 20 minutes. Remove from the oven and let cool slightly. Invert onto a rack and cool. Invert so top is up. Cut into 1 3/4-inch squares.