Preheat oven to 325°F. Coat an 8-inch square baking pan with cooking spray. Line the bottom and 2 sides with parchment paper, leaving a 2-inch overhang; coat the parchment with cooking spray.

Combine 2 cups plus 1 tablespoon milk and the cubed butter in a medium saucepan. Cook over medium-low heat until the butter is melted, about 5 minutes. Do not boil. Remove from heat and set aside.

Beat the 4 egg whites in a large bowl with an electric mixer on medium-high speed until stiff peaks form, about 4 minutes.

In another large bowl, combine the 4 egg yolks, ⅔ cup granulated sugar, 2 tablespoons lemon zest, 2 teaspoons vanilla and ¼ teaspoon salt; beat on high speed until pale and creamy, 2 to 3 minutes. Add ¼ cup plus 1 tablespoon all-purpose flour and ¼ cup plus 1 tablespoon whole-wheat flour; beat on low speed until a thick batter forms, about 1 minute.

Gradually add the warm milk mixture to the batter, beating on low speed until fully incorporated, about 1 minute. Let stand for 10 minutes.

Gently whisk the beaten egg whites into the batter until mostly incorporated and no large lumps remain. Do not overmix; the batter will be foamy on top.

Pour the batter into the prepared pan. Bake until the top is golden, the edges are just pulling away from the sides and the center still jiggles slightly, about 50 minutes.

Let cool in the pan on a wire rack for 30 minutes. Refrigerate until set, about 1 hour. Dust with 2 tablespoons confectioners’ sugar. Garnish with additional lemon zest, if desired. Cut into 9 squares and serve chilled or at room temperature.