To prepare cake: Preheat oven to 350 degrees F. Coat two 9-inch round cake pans with cooking spray with flour (see Tip); alternatively, coat the pans with regular cooking spray, line them with parchment paper and spray the paper.

Whisk all-purpose flour, whole-wheat flour and salt in a medium bowl.

Beat 4 eggs and 2/3 cup sugar in a large bowl with an electric mixer on medium-high speed until pale yellow and doubled in volume, 5 to 10 minutes. Beat in vanilla and 1 teaspoon lime zest.

With a rubber spatula, gently fold almond (or canola) oil into the egg mixture, using long, even strokes, until just incorporated. Add the flour mixture; gently stir until just incorporated. Divide the batter between the pans; spread to the edges and gently rap the pans against the counter once or twice to settle the batter.

Bake, rotating the pans halfway through, until lightly browned and a toothpick inserted into the center comes out clean, 20 to 22 minutes. Cool on a wire rack for 10 minutes, then invert the layers onto the rack, remove the pans and parchment paper, if using, and let cool completely, about 45 minutes.

To prepare lime filling: Whisk condensed milk, lime juice and 1 teaspoon lime zest in a medium bowl until combined. Refrigerate until thickened, at least 30 minutes or overnight.

To prepare meringue: Beat egg whites in a medium bowl with an electric mixer at high speed until soft peaks form. Beat in 1/4 cup sugar in a slow, steady stream. Continue beating until stiff peaks form.

Position oven rack about 6 inches from the heat source; preheat broiler. Transfer one layer, bottom-side down, to a large baking sheet. Spread the meringue on top of the cake, creating decorative peaks and valleys in the meringue with a rubber spatula. Broil until lightly browned, watching carefully to prevent burning, 30 seconds to 1 minute.

To assemble cake: Place the plain layer, top-side down, on a serving plate; spread the lime filling on top. Cover with the meringue-topped layer.