Preheat oven to 350°F. Line an 8x8-inch baking pan with parchment paper leaving a 2-inch overhang along each side.
Combine white chocolate and butter in a heatproof bowl and place it over a saucepan with barely simmering water. Stir until completely melted and smooth. Or, melt in the microwave at 50% power in short bursts with frequent stirring so that it doesn't burn.
Combine eggs, sugar, lemon zest and salt in a large bowl and whisk or beat with an electric hand mixer until pale and thick. Mix in vanilla. Mix in warm melted white chocolate mixture.
Sprinkle in flour and fold it in gently. Just before all of the flour is incorporated, fold in the chocolate chips.
Spread the batter evenly into prepared pan and bake for 22-26 minutes until the top is shiny and crackly. Transfer to a wire rack to cool completely.
For the glaze, combine chopped white chocolate and lemon juice in a bowl and place it over a saucepot with ½ inch of barely simmering water. Stir until smooth and glossy. You can also do this in the microwave, but make sure to stop every 15-20 seconds to stir so it doesn't burn. Immediately drizzle over cooled brownies and let set for about 15 minutes before slicing.
