Preheat the oven to 350°F. Grease and line an 8x8 baking pan with parchment paper. Set aside.
Place the butter and white chocolate in a microwave safe bowl. Microwave for 1 minute, then stir to fold in the melted butter with the chocolate. Continue to cook in 20-30 second increments, stirring in between until everything is completely melted. Set aside to cool.
Combine the sugar and lemon zest in a large mixing bowl, rubbing the sugar and zest between your fingertips to release the oils in the lemon. Add the eggs, egg yolk, and vanilla, stirring with a whisk until completely combined. Then fold in the slightly cooled white chocolate mixture.
Add the flour, salt, and baking powder to the wet ingredients, folding gently with a rubber spatula. Last, stir in the fresh lemon juice, mixing only until incorporated. Pour into the prepared pan.
Bake for ~22-25 minutes. The edges will look golden brown, (the tops won't be browned), and a toothpick inserted in the center should come out mostly clean, a few moist crumbs are what you want. Allow to cool completely.