Position a rack in the center of the oven and preheat to 325°F (165°C). Line a large baking sheet with parchment paper.
Measure the coconut and condensed milk carefully. If the coconut strands are especially long, chop them briefly into shorter pieces without grinding them into powder.
In a large bowl, stir together the shredded coconut, sweetened condensed milk, vanilla, and salt until evenly combined. The mixture should be thick and sticky, with no pool of condensed milk at the bottom.
Place the egg white in a separate, clean, grease-free bowl. Beat with an electric mixer until firm, glossy peaks form. The peak should hold its shape when the beaters are lifted. Stop before the white becomes dry or clumpy.
Fold about one-third of the beaten egg white into the coconut mixture to loosen it slightly. Gently fold in the remainder until no visible streaks remain.
Divide the mixture into 15 equal portions, approximately 32–33 g each. Use a small scoop or two spoons to form rounded mounds on the lined baking sheet, leaving approximately 1½ inches between them.
Gently tuck loose coconut strands against each mound. Shape just firmly enough to hold the cookies together without compressing them into dense balls.
Bake for approximately 20–25 minutes, rotating the baking sheet after about 12 minutes. The bases and exposed coconut tips should be golden, while the centers remain pale and the mounds hold their shape.
Let the cookies cool on the baking sheet for 10 minutes. They will be fragile when first removed from the oven.
Transfer carefully to a wire rack and cool for at least another 10 minutes, or until firm enough to handle. Serve once cooled.