With the rack in the middle position, preheat the oven to 350°F (180°C). Butter and line the bottom of two 8-inch (20 cm) springform pans with parchment paper. Set aside.
In a bowl, combine the flour and baking powder. Set aside.
In another bowl, beat the eggs, sugar and vanilla extract with an electric mixer for 10 minutes or until the mixture triples in volume and forms a ribbon as it falls from the beaters. At low speed, drizzle in the oil. With a whisk or spatula, gently fold in the dry ingredients.
Spoon the batter into the prepared pans and bake for about 30 minutes or until a toothpick inserted into the centre of the cakes comes out clean. Let cool completely. Unmould.
Strawberry Rhubarb Compote
Meanwhile, in a saucepan, combine all the ingredients. Bring to a boil over medium heat, stirring constantly, and let simmer for 5 minutes. Transfer to a bowl. Cover with plastic wrap directly on the surface of the compote and let cool. Refrigerate for 4 hours or until completely chilled.
In a bowl, whip the cream, sugar and vanilla extract until stiff peaks form. Set aside in the refrigerator.
Slice each cake in half horizontally to make 4 slices. Spread the compote over 3 slices and stack. Cover with the last slice. Completely ice the cake with the whipped cream. Refrigerate for 2 hours before serving. Even better the next day.