Preparing your oven - Preheat your oven to 170C / 340F (fan off), 150C / 300F (fan on). Or an even rise, bake with no fan. Position your rack in the middle of the oven. Make sure your oven is fully preheated before making the batter.
Preparing your cake tins - Spray a loaf tin 25 x 10cm / 10 x 4-inch and a square baking tin 20 x 20cm / 8 x 8-inch with oil spray and line the bottom and sides with baking paper. Set aside.
Combine dry ingredients - Whisk the flour, baking powder and salt in a medium sized bowl until combined. Set aside.
Beat the eggs and sugar - Add the eggs to a large mixing bowl (glass or metal) and use an electric mixer to beat until frothy, about 1 minute. A stand mixer with a whisk attachment also works. With the mixer on medium-high speed, add the sugar a spoonful at a time, taking about 1 minute to add it all. Once all the sugar is added, keep beating on medium-high speed for 6 minutes until the mixture is pale, thick, and tripled in size.
Add dry ingredients to egg mixture - Add half the dry ingredients to the egg mixture and mix on low speed until just combined. Repeat with the rest. The batter will be thick. Avoid overmixing the batter, small lumps are fine, they’ll disappear in the next step.
Heat milk and butter - Heat the milk and butter in a saucepan over medium heat, stirring continuously, until it reaches 60°C/140°F or small bubbles form around the edges. Do not let it boil.
Add hot milk - Add half the hot milk mixture, along with the oil and vanilla. Mix on low speed until combined. Add the rest of the milk mixture and mix again until smooth. The batter will be thin and pour in a steady ribbon.
Divide the batter - Add 600g of batter into the loaf tin and the rest of the batter (about 930g) into the square baking tin. Tap each tin on the counter three times to release air bubbles.
Bake - Bake both on the middle rack of your oven. The square cake will take about 30 minutes to bake. The loaf cake will take an extra 5-10 minutes to finish baking. You’ll know they’re baked when a toothpick inserted in the center comes out clean. The cakes should be deep golden and spring back when lightly touched. If they sink and don’t spring back, bake for a couple more minutes until ready.
Cool the cakes - Let them cool in the tins for 10 minutes, then run a knife around the edges to loosen. Transfer to a cooling rack, placing them baking paper side down, and let them cool completely.