Preheat the oven to 325 degrees F and line a large baking sheet with parchment paper. Stir the shredded coconut, sweetened condensed milk, vanilla extract, and fine salt together.
Beat the aquafaba and cream of tartar with an electric mixer for 4 to 6 minutes, until glossy medium peaks form.
Fold one-third of the whipped aquafaba into the coconut mixture to lighten it. Gently fold in the remaining aquafaba until evenly incorporated.
Portion the mixture into 18 compact mounds on the prepared baking sheet. Gently shape the sides so loose coconut strands do not burn.
Bake for 20 to 25 minutes, until the edges and peaks are deeply golden. Cool completely on the baking sheet so the centers become chewy.
Melt the chopped chocolate with the coconut oil, stirring until smooth. Dip the bottoms of the cooled macaroons into the chocolate and return them to the parchment.
Drizzle any remaining chocolate over the tops. Let the macaroons stand until the chocolate is fully set.