Eggs have rising properties for cakes, breads and brioches, as well as binding and moisturizing roles for certain types of cookies, quiches and pies. Sometimes, you might need to replace eggs, whether for a personal choice (becoming vegan, for example) or in an emergency, when we have a sudden desire for cake but no eggs left in the house.
There are plenty of possible combinations that can replace eggs in recipes (water + agar agar, tofu, flax seeds + water, etc), but let us simplify it a step further. You can actually replace eggs with applesauce. Substitute about 1.75 ounces of applesauce for 1 egg. Or you can use a mashed overripe banana. In this case, use 1/2 a banana for 1 egg.
Speaking of applesauce, you might or might not have already known that the fats in your recipes can be replaced with this healthier fruit-based substitute! Try this cookie recipe made with just 3 ingredients: 1 1/3 cup flour + applesauce + 1 instant-yeast packet. You can always add dried fruits or chocolate chips for extra flavor. And if you're avoiding butter, applesauce is a commonly used substitute in numerous cake recipes!