In a small bowl or on waxed paper, stir together the flour, cinnamon, baking soda, and salt. Set aside.
In a large bowl, beat the eggs until foamy. Then beat in the oil, sugar, and vanilla. Stir the flour mixture into the wet ingredients until blended. Then stir in the apples and walnuts.
Spoon the batter into 2 1/2-inch muffin tins lined with paper muffin cups. Bake for 15 to 20 minutes or until a pick inserted in the center comes out clean. Remove from pans and serve warm or at room temperature.