Preheat your oven to 180°C (350°F). Line a 9x9-inch square baking pan with parchment paper.
In a heat-safe mixing bowl, combine butter and chopped white chocolate. Melt in the microwave in 20-second bursts (or over a double boiler), stirring until smooth. Let cool for 5 minutes.
Whisk in granulated sugar, lemon zest, fresh lemon juice, oil, room-temperature eggs, vanilla extract, and salt until smooth and combined.
Add all-purpose flour and fold with a rubber spatula just until no dry flour streaks remain. Do not overmix.
Pour batter into the prepared pan and spread evenly. Bake for 20 to 30 minutes, until the top is set and a toothpick inserted in the center comes out with a few moist crumbs.
Cool in the pan for 1 hour. In a small bowl, whisk powdered sugar, lemon juice, lemon zest, and milk until smooth. Spread over cooled brownies, let set for 10 minutes, then slice.
Notes
Measure Flour Accurately: Fluff flour with a fork, spoon it into your measuring cup, and sweep flat with a knife (or weigh 125g / 1 cup). Packing flour directly from the bag will result in cakey brownies.
Room-Temperature Eggs: Use room-temperature eggs so they blend smoothly. Cold eggs can cause the melted white chocolate and butter to seize up.
Fresh Lemons Only: Use freshly squeezed lemon juice and fresh zest. Bottled lemon juice lacks the natural oils and acidity required for bright citrus flavor.
Avoid Overbaking: Remove from the oven when edges are set and a toothpick inserted in the center comes out with a few moist crumbs. They will continue to set as they cool.
Cool Before Glazing: Let the brownies cool completely in the pan for at least 1 hour before adding the glaze; otherwise, the icing will melt into a liquid.
Clean Slicing: Use the parchment paper overhang to lift the brownies out of the pan. Slice with a sharp chef’s knife, wiping the blade clean between cuts.
Storage: Store in an airtight container at room temperature for up to 2 days, or refrigerate for up to 5 days. Wrap unglazed slices and freeze for up to 2 months.