Preheat oven to 350 degrees F (175 degrees C). Grease a 9-inch fluted-tube pan (such as Bundt®).
Whisk eggs, brown sugar, oil, and vanilla extract together in a bowl until smooth.
Sift flour, baking soda, salt, cinnamon, and nutmeg together in a separate bowl; stir into egg mixture. This is a very thick mixture so use a solid spoon to mix together. Fold in apples, cranberries, and pecans until evenly incorporated. Pour batter in the prepared pan.
Bake in the preheated oven until a toothpick inserted in the center of the cake comes out clean, about 1 hour 15 minutes.