Preheat the oven to 325ºF (165ºC). Line an 8-inch square baking pan** with parchment paper, leaving a couple of inches of overhang.
Place the butter in a heat-safe bowl placed over a pan of barely simmering water, making sure the water doesn't touch the bottom of the bowl. When the butter is melted, turn off the heat and add the white chocolate. Let stand for 3-4 minutes, then stir gently until smooth and melted. (Alternately you can melt the butter in the microwave.)
In a large bowl, whisk together the sugar, lemon zest, eggs, egg yolk, lemon juice, oil, salt and vanilla until the sugar is dissolved and the mixture is creamy and well blended. Stir in the melted butter and white chocolate mixture until well combined. Stir in the flour just until combined.
Transfer the batter to the baking pan. Smooth the top with a spatula. Bake until a toothpick inserted into the center of the brownies comes out with a few moist crumbs on it (not wet batter), about 18-23 minutes. Be careful not to over bake your brownies, as this will dry them out. Let the brownies cool in the pan.