Preheat oven to 350°F. Line an 8-inch square pan with parchment, leaving an overhang. Lightly grease the sides.
Whisk melted butter with brown sugar and granulated sugar until smooth and glossy.
Whisk in the egg and vanilla until fully combined.
In a separate bowl, whisk flour, baking powder, salt, and lemon zest. Remove 1 teaspoon of this mix to a small dish for the berries.
Stir the dry ingredients into the butter mixture just until a few flour streaks remain.
Toss blueberries with the reserved flour. Fold blueberries and white chocolate chips into the batter gently.
Spread batter evenly in the pan and smooth the top.
Bake 26–30 minutes, until the edges are set and a toothpick comes out with a few moist crumbs.
Cool completely in the pan on a rack. Lift out using parchment and cut into 12 bars.