Preheat the oven to 340°F (170°C). Line a 9×13 pan with parchment so the cake bakes in a thin sheet.
Weigh 115 g (½ cup) unsalted butter, then brown it:
Add the butter to a small saucepan and cook over medium heat until it foams, sizzles, and turns a medium-amber color. Remove from heat and let cool for 5–7 minutes so it’s warm-liquid, not sizzling hot.
In a medium bowl, whisk together the 160 g (1 ⅓ cups) cake flour, 1 ½ tsp baking powder, ¼ tsp fine sea salt, and 1 Tbsp cornstarch.
In a separate bowl, whisk the browned butter with 150 g (¾ cup) granulated sugar until glossy and combined.
Whisk in the 2 large eggs, one at a time, then add 2 tsp vanilla extract.
Add half the dry mixture → whisk gently.
Add 120 ml (½ cup) whole milk → whisk again.
Add the remaining dry mixture → whisk just until smooth and combined. Do not overmix.
Pour the batter into the prepared pan and use an offset spatula to spread it into a thin, even layer.
Tap on the counter a few times to help level out the batter.
Bake for 16 minutes, or until the top is set, soft, and lightly springy. Avoid overbaking — the cake should stay tender for layering.
Cool completely in the pan before cutting or assembling.
