Place the pitted Medjool dates into the bowl of a food processor. Pulse until the dates form a thick, sticky paste.
Add 1 cup of the shredded coconut, the fresh lime zest, lime juice, sea salt, and vanilla extract to the processor.
Pulse the mixture repeatedly until the ingredients are well combined and the dough begins to clump together around the blade.
Remove the blade carefully and scoop out tablespoon-sized portions of the mixture using your hands or a small cookie scoop.
Roll each portion between your palms to create smooth, round spheres.
Place the remaining 1/2 cup of shredded coconut into a small bowl. Roll each sphere in the coconut until it is evenly coated.
Arrange the finished bites on the parchment-lined plate and refrigerate for at least 30 minutes to firm up the texture before serving.