Butter a 9x13-inch (23x33 cm) baking pan, then coat it with breadcrumbs.
Clean the apricots and raspberries, then pat them dry with paper towels. Tear the apricots in half and remove the stones.
10 apricots, 1 cup raspberries
Preheat your oven to 350°F (175°C).
Separate the eggs into egg whites and egg yolks (the safest way is to do this with your hands). Place the egg whites in a medium/large bowl and the yolks in a large bowl.
5 large eggs
We need to beat the egg yolks and egg whites separately. If you have two mixers, you can do this at the same time—egg whites in a stand mixer fitted with a whisk attachment, and egg yolks with a hand mixer. If you only have one mixer, beat the egg whites first, then use the same whisk to beat the egg yolks. (Remember: the whisk and bowl must be perfectly clean before beating the egg whites, or they won’t whip properly.)
Add about half of the sugar (just eyeball it) to the egg yolks, along with the lemon zest and vanilla. Beat with a mixer for about 2-3 minutes, until the mixture becomes pale and creamy, with ribbons forming from the yolk mixture when lifted.
1 cup + 2 tablespoons (225g) granulated sugar, 2 teaspoons vanilla extract, zest grated from 1 lemon
In the stand mixer, whip the egg whites until foamy, then gradually add the remaining sugar while continuing to whip until stiff peaks form.
Add the oil to the egg yolk mixture, then mix in the baking powder and salt.
3 tablespoons vegetable oil, 1 teaspoon baking powder, 1/4 teaspoon salt
Gently fold in 1/3 of the beaten egg whites into the egg yolk mixture, then add the flour. Carefully fold in the remaining egg whites until just combined.
1 1/2 cups (190g) all-purpose flour
Pour the batter into the prepared pan and smooth the surface.
Prepare a small bowl with a little flour. Dip the bottom of each apricot half in the flour and place them on top of the batter—4 halves along the short edge and 5 halves along the long edge. Don't press the fruit in! If your apricots vary in size, place the larger ones at the edges and the smaller ones in the middle.
Dip the pointed end of each raspberry in the flour, then place them between the apricot halves. Ensure the raspberries don’t touch the walls of the baking pan, as they may burn slightly.
Bake the cake for about 45 minutes, or until a toothpick inserted into the center comes out mostly clean, with a few small crumbs attached.
Let the cake cool just slightly - it tastes best when just slightly warm from the pan.
Sprinkle the cake generously with powdered sugar, cut it into squares, and enjoy!