Preheat the oven to 160C. Grease and line a 7-inch round or loaf cake pan with parchment paper.
Beat the eggs and sugar in a large mixing bowl using a whisk or hand mixer until the mixture is pale, thick, and fluffy.
Add the oil and mix until well combined.
Sift together the flour, baking powder, and salt. Gradually fold the dry ingredients into the wet mixture until just incorporated. Do not overmix.
In a small saucepan, heat the milk and butter over low heat until the butter is melted and the mixture is hot but not boiling. Remove from heat and stir in the vanilla essence.
Slowly pour the hot milk mixture into the cake batter while gently stirring. Mix until smooth and well combined.
Pour the batter into the prepared cake pan and smooth the top.
Bake for 30-35 minutes, or until a toothpick inserted into the center comes out clean.
Cool the cake in the pan for 10 minutes, then transfer to a wire rack to cool completely.
