Preheat oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking pan.
Melt the butter and white chocolate together over low heat in a saucepan. Remove from heat, and let cool slightly. Meanwhile beat eggs with sugar and vanilla extract in a mixing bowl; mix in the butter mixture, and stir in the flour and salt until thoroughly combined. Scoop the batter into the prepared baking pan; sprinkle with white chocolate chips.
Bake in the preheated oven until a toothpick inserted into the center of the pan comes out clean, 30 to 35 minutes. Allow to cool in pan for about 10 minutes before cutting into bars.
