In a small bowl or on waxed paper, stir together flour, cinnamon, baking soda, and salt; set aside. In a large bowl beat eggs until foamy; beat in oil, sugar, and vanilla. Stir in flour mixture until blended; stir in apples and nuts.
Spoon into 2 1/2-inch muffin tins lined with paper muffin cups. Bake in preheated 350-degree oven 15 to 20 minutes or until pick inserted in center comes out clean. Remove from pans; serve warm or at room temperature.