Preheat your oven to 350 degrees F. Line a rimmed baking sheet with parchment paper.
Whisk together the eggs, coconut oil, stevia, and vanilla. The coconut oil might harden when it comes in touch with the cold eggs. That’s OK. Mix as best as you can and don’t worry if the mixture is a bit lumpy.
Stir in the shredded coconut with a fork or a rubber spatula. Make sure the coconut is well-moistened. If the mixture is very dry and crumbly, you might need to add a tablespoon or two of water.
Scoop 1.5-tablespoon portions of the mixture (using a standard cookie scoop) onto the parchment paper. Pack the mixture into the scoop. Very lightly flatten the tops if you wish. The cookies won’t expand while they bake, so you can space them close to each other, but don’t let them touch.
Bake the cookies until golden, about 12 minutes at 350 degrees F. Some of the oil will seep into the pan (that's why we're using a rimmed baking sheet). Let the cookies rest and cool in the pan for 10 minutes to absorb back some of it, then remove them from the pan into a serving plate.
Let the cookies cool completely, 20 more minutes, before enjoying them. Store in an airtight container on the counter for up to three days. They actually improve with storage and become less dry and chewier.
*Shredded coconut products greatly vary in their moisture content, so 2 cups won't always weigh 4 oz. If this is the case for you, I suggest using two measuring cups (240 ml) of whatever product you have. Then, if the mixture ends up dry, add water, one tablespoon at a time. Make sure you don't use reduced-fat shredded coconut. It's extremely dry and will produce cookies that will go straight to the trash - and I'm speaking from a sad experience.Generally speaking, unsweetened coconut is drier than sweetened. But try to get a brand that looks as moist as possible.