Preheat the oven to 180°C (350°F). Grease the pan, lightly flour it, and shake off any excess.
Cut the butter into cubes. Heat it in the microwave for 20 seconds, stir, and repeat in short intervals until the butter is fully melted. Set aside to cool.
Mix the flour and cinnamon thoroughly with a spoon and set aside.
Peel and core the apples. Cut them into quarters and slice each quarter lengthwise into 3 mm thick slices. Transfer 12 slices to a bowl, add 1 tablespoon of lemon juice, and mix well.
Cut the remaining slices into 1×1 cm cubes. Place them in a separate bowl, add the remaining lemon juice, and mix well.
Fit a mixer with the whisk attachment. Place the eggs in the mixer bowl and whip on high speed for about 30 seconds. Add the sugar and vanilla extract, and whip for 10 minutes until a light, fluffy mixture forms. Stop the mixer.
Replace the whisk with the paddle attachment (or continue using a spatula). Turn the mixer to the lowest speed and alternate adding the flour (about a third at a time) and the milk (half the amount at a time) to the whipped eggs. Once the batter is silky smooth, slowly add the melted butter (or oil) in a thin stream, followed by the diced apple cubes. Mix for a few more seconds, just until the batter is uniform.
Pour the batter into the pan and smooth the top. Arrange the 12 apple slices evenly over the batter, standing each slice upright with the curved side facing up and half-submerged in the batter.
Sprinkle the demerara sugar evenly over the cake and bake for 35-40 minutes, or until a toothpick inserted in the center comes out clean. Once the cake has cooled, dust it with powdered sugar.
