Preheat the oven to 325 degrees Fahrenheit.

In a mixing bowl, combine eggs, sugar, and vanilla.

Mix until the mixture is light and fluffy.

Add the flour, baking powder, and salt to the egg mixture.

Mix the dry and wet ingredients well.

Gently fold in the chopped apples and walnuts.

Grease a 9x9 inch baking dish to prevent sticking.

Pour the batter into the prepared baking dish.

Bake in the preheated oven for approximately 30 minutes, or until a toothpick inserted into the center comes out clean.

Let the pudding cool slightly before serving.

Serve warm.