With the rack in the middle position, preheat the oven to 180°C (350°F). Line a 30 x 43-cm (12 x 17-inch) baking sheet with parchment paper, allowing the paper to hang over the ends. Generously butter the paper and unlined sides.
In a bowl, combine the flour, baking powder and salt. Set aside.
In another bowl and using an electric mixer, cream the butter with the sugar and vanilla. Add the egg whites and beat until just incorporated. With the mixer on low, add the dry ingredients, alternating with the milk.
Spread the batter evenly over the baking sheet. Bake until a toothpick inserted in the centre comes out clean, about 20 minutes. Let cool partially and unmould onto a cooling rack. Cover with a clean tea towel and let cool completely.
Meanwhile, in a saucepan, bring the maple syrup, cream and corn syrup to a boil. Simmer until a candy thermometer reads 117°C (242°F), 5 to 10 minutes.
While beating with an electric mixer on medium, pour the hot syrup in a thin stream onto the egg yolks, taking care not to pour it on the beaters. Beat until completely cooled, about 15 minutes.
Add the butter, 1 or 2 pieces at a time, beating until the buttercream is very thick (see note, above). Pause several times to scrape the bottom of the bowl with a spatula.
Trim the edges of the cake so they are straight and even. Trim the top if bulging. Cut the cake into 4 rectangles.
Ice each layer with 125 ml (1/2 cup) buttercream, stacking the layers as you go. Ice the assembled cake.
Recipes with the "Healthy Pick" stamp have been evaluated by a registered dietitian member of the Ordre professionnel des diététistes du Québec.