Preheat the oven to 180°C (350°F). Grease and lightly flour a 9x13 inch (33 cm) baking pan.
In a large bowl, beat the eggs, sugar, and vanilla with an electric mixer until pale and thick. Mix in the oil and milk.
Sift the flour and baking powder into the bowl. Fold gently until just combined.
In a separate bowl, mix the chopped apples, walnuts, brown sugar, and cinnamon.
Pour the batter into the prepared pan. Spread the apple-walnut mixture evenly over the top.
Bake for 50-55 minutes, or until a toothpick inserted into the center of the cake comes out clean.
Let cool in the pan for 20 minutes before slicing. Serve warm or at room temperature.
