Preheat the oven to 350°F / 175°C. Line the bottoms of two 9-inch / 23cm cake pans with greased parchment, but leave the sides of the pans untouched. The cakes need to cling to the ungreased pans to rise properly.
In a large bowl, whisk together the flour, baking powder, and salt and then sift back into the bowl. Set aside.
In a stand mixer fitted with the whisk attachment, whip the eggs and egg yolks on high speed. Once the eggs are well combined and starting to foam, about 1 minute, turn the speed to medium-low and sprinkle 3 ⁄4 cup / 150g of the sugar slowly over top. Turn the speed to high and let it whip for about
5 minutes.
While the eggs are whipping, in a small saucepan over medium heat, bring the milk, oil, and remain- ing 3 ⁄4 cup / 150g sugar to a boil. Turn off the heat and stir in the vanilla.
Once the eggs are light in color and thick, they should be able to form a ribbon of batter that sits on top of the egg foam for a few seconds when you lift the whisk out of the foam. Turn the mixer speed to low, slowly add the boiling milk mixture, and then add the flour mixture, a few tablespoons at a time, scraping down the bowl several times.
Immediately pour the batter into the prepared pans and gently run a spatula through the batter to pop any large air bubbles.
Bake until a tester comes out clean, 15 to 20 minutes. Let the cake cool completely in the pans. Run a knife around the edge before turning out onto serving plates. The cakes can be served simply sliced with dollops of lemon curd.