In a bowl, add the milk and eggs and whisk until the eggs and milk are fully incorporated.
Season with salt and pepper to your taste and whisk to combine. Then, pour in the oil and whisk well to incorporate as best you can.
Next sift in the flour, baking powder, and parmesan. If there are any large bits of parmesan that won’t go through even after breaking up the chunks, you can just add them into the batter anyway. Gently whisk together until fully incorporated.
Prepare your vegetables by lightly tossing them in flour. This helps prevent them from sinking during the baking process.
Next, prepare your baking pan with butter and flour then spoon in about 1 cup of batter. Lay down one layer of vegetables, then cover with more batter. Repeat this pattern until you’ve finished adding the batter to the pan. Top the batter with more vegetables and pipe a line of softened butter down the middle.
Bake at 180°C/350°F for 35-45 minutes. The baking time will vary depending on your oven, so just keep an eye out for when the top starts to brown. Be careful, too, as some vegetables on top may start to burn before the rest is cooked.
Once a skewer/toothpick inserted comes out clean, remove from the oven and let cool on a cooling rack. Once warm to the touch, you can remove the cake salé from the pan and let it cool completely on the rack.
Wait until the cake salé is completely cool, so you can slice into it cleanly, and the cake salé is done! 完成です!